Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II

Abstract This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multi-dimensional case, we consider only...
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Autor*in:	Ikoma, Norihisa [verfasserIn] Ishii, Hitoshi [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	Eigenvalue problem Fully nonlinear equation General boundary conditions Principal eigenvalues Higher order eigenvalues

Übergeordnetes Werk:	Enthalten in: Bulletin of mathematical sciences - [Cham] : Springer International Publishing, 2011, 5(2015), 3 vom: 25. Juli, Seite 451-510
Übergeordnetes Werk:	volume:5 ; year:2015 ; number:3 ; day:25 ; month:07 ; pages:451-510

Links:	Volltext

DOI / URN:	10.1007/s13373-015-0071-0

Katalog-ID:	SPR032087357

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520			\|a Abstract This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multi-dimensional case, we consider only radial eigenpairs. Our eigenvalue problem has a general first-order boundary condition which includes, as a special case, the Dirichlet, Neumann and Robin boundary conditions. Given a nonnegative integer n, we prove the existence and uniqueness, modulo multiplication of the eigenfunction by a positive constant, of an eigenpair whose eigenfunction, as a radial function in the multi-dimensional case, has exactly n zeroes. When an eigenfunction has n zeroes, we call the corresponding eigenvalue of nth order. Furthermore, we establish results concerning comparison of two eigenvalues, characterizations of nth order eigenvalues via differential inequalities, the maximum principle for the boundary value problem in connection with the principal eigenvalue, and existence of a solution having n zeroes, as a radial function in the multi-dimensional case, of the boundary value problem with an inhomogeneous term.
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allfields	10.1007/s13373-015-0071-0 doi (DE-627)SPR032087357 (SPR)s13373-015-0071-0-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE Ikoma, Norihisa verfasserin aut Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multi-dimensional case, we consider only radial eigenpairs. Our eigenvalue problem has a general first-order boundary condition which includes, as a special case, the Dirichlet, Neumann and Robin boundary conditions. Given a nonnegative integer n, we prove the existence and uniqueness, modulo multiplication of the eigenfunction by a positive constant, of an eigenpair whose eigenfunction, as a radial function in the multi-dimensional case, has exactly n zeroes. When an eigenfunction has n zeroes, we call the corresponding eigenvalue of nth order. Furthermore, we establish results concerning comparison of two eigenvalues, characterizations of nth order eigenvalues via differential inequalities, the maximum principle for the boundary value problem in connection with the principal eigenvalue, and existence of a solution having n zeroes, as a radial function in the multi-dimensional case, of the boundary value problem with an inhomogeneous term. Eigenvalue problem (dpeaa)DE-He213 Fully nonlinear equation (dpeaa)DE-He213 General boundary conditions (dpeaa)DE-He213 Principal eigenvalues (dpeaa)DE-He213 Higher order eigenvalues (dpeaa)DE-He213 Ishii, Hitoshi verfasserin aut Enthalten in Bulletin of mathematical sciences [Cham] : Springer International Publishing, 2011 5(2015), 3 vom: 25. Juli, Seite 451-510 (DE-627)654743967 (DE-600)2599335-5 1664-3615 nnns volume:5 year:2015 number:3 day:25 month:07 pages:451-510 https://dx.doi.org/10.1007/s13373-015-0071-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2015 3 25 07 451-510
spelling	10.1007/s13373-015-0071-0 doi (DE-627)SPR032087357 (SPR)s13373-015-0071-0-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE Ikoma, Norihisa verfasserin aut Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multi-dimensional case, we consider only radial eigenpairs. Our eigenvalue problem has a general first-order boundary condition which includes, as a special case, the Dirichlet, Neumann and Robin boundary conditions. Given a nonnegative integer n, we prove the existence and uniqueness, modulo multiplication of the eigenfunction by a positive constant, of an eigenpair whose eigenfunction, as a radial function in the multi-dimensional case, has exactly n zeroes. When an eigenfunction has n zeroes, we call the corresponding eigenvalue of nth order. Furthermore, we establish results concerning comparison of two eigenvalues, characterizations of nth order eigenvalues via differential inequalities, the maximum principle for the boundary value problem in connection with the principal eigenvalue, and existence of a solution having n zeroes, as a radial function in the multi-dimensional case, of the boundary value problem with an inhomogeneous term. Eigenvalue problem (dpeaa)DE-He213 Fully nonlinear equation (dpeaa)DE-He213 General boundary conditions (dpeaa)DE-He213 Principal eigenvalues (dpeaa)DE-He213 Higher order eigenvalues (dpeaa)DE-He213 Ishii, Hitoshi verfasserin aut Enthalten in Bulletin of mathematical sciences [Cham] : Springer International Publishing, 2011 5(2015), 3 vom: 25. Juli, Seite 451-510 (DE-627)654743967 (DE-600)2599335-5 1664-3615 nnns volume:5 year:2015 number:3 day:25 month:07 pages:451-510 https://dx.doi.org/10.1007/s13373-015-0071-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2015 3 25 07 451-510
allfields_unstemmed	10.1007/s13373-015-0071-0 doi (DE-627)SPR032087357 (SPR)s13373-015-0071-0-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE Ikoma, Norihisa verfasserin aut Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multi-dimensional case, we consider only radial eigenpairs. Our eigenvalue problem has a general first-order boundary condition which includes, as a special case, the Dirichlet, Neumann and Robin boundary conditions. Given a nonnegative integer n, we prove the existence and uniqueness, modulo multiplication of the eigenfunction by a positive constant, of an eigenpair whose eigenfunction, as a radial function in the multi-dimensional case, has exactly n zeroes. When an eigenfunction has n zeroes, we call the corresponding eigenvalue of nth order. Furthermore, we establish results concerning comparison of two eigenvalues, characterizations of nth order eigenvalues via differential inequalities, the maximum principle for the boundary value problem in connection with the principal eigenvalue, and existence of a solution having n zeroes, as a radial function in the multi-dimensional case, of the boundary value problem with an inhomogeneous term. Eigenvalue problem (dpeaa)DE-He213 Fully nonlinear equation (dpeaa)DE-He213 General boundary conditions (dpeaa)DE-He213 Principal eigenvalues (dpeaa)DE-He213 Higher order eigenvalues (dpeaa)DE-He213 Ishii, Hitoshi verfasserin aut Enthalten in Bulletin of mathematical sciences [Cham] : Springer International Publishing, 2011 5(2015), 3 vom: 25. Juli, Seite 451-510 (DE-627)654743967 (DE-600)2599335-5 1664-3615 nnns volume:5 year:2015 number:3 day:25 month:07 pages:451-510 https://dx.doi.org/10.1007/s13373-015-0071-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2015 3 25 07 451-510
allfieldsGer	10.1007/s13373-015-0071-0 doi (DE-627)SPR032087357 (SPR)s13373-015-0071-0-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE Ikoma, Norihisa verfasserin aut Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multi-dimensional case, we consider only radial eigenpairs. Our eigenvalue problem has a general first-order boundary condition which includes, as a special case, the Dirichlet, Neumann and Robin boundary conditions. Given a nonnegative integer n, we prove the existence and uniqueness, modulo multiplication of the eigenfunction by a positive constant, of an eigenpair whose eigenfunction, as a radial function in the multi-dimensional case, has exactly n zeroes. When an eigenfunction has n zeroes, we call the corresponding eigenvalue of nth order. Furthermore, we establish results concerning comparison of two eigenvalues, characterizations of nth order eigenvalues via differential inequalities, the maximum principle for the boundary value problem in connection with the principal eigenvalue, and existence of a solution having n zeroes, as a radial function in the multi-dimensional case, of the boundary value problem with an inhomogeneous term. Eigenvalue problem (dpeaa)DE-He213 Fully nonlinear equation (dpeaa)DE-He213 General boundary conditions (dpeaa)DE-He213 Principal eigenvalues (dpeaa)DE-He213 Higher order eigenvalues (dpeaa)DE-He213 Ishii, Hitoshi verfasserin aut Enthalten in Bulletin of mathematical sciences [Cham] : Springer International Publishing, 2011 5(2015), 3 vom: 25. Juli, Seite 451-510 (DE-627)654743967 (DE-600)2599335-5 1664-3615 nnns volume:5 year:2015 number:3 day:25 month:07 pages:451-510 https://dx.doi.org/10.1007/s13373-015-0071-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2015 3 25 07 451-510
allfieldsSound	10.1007/s13373-015-0071-0 doi (DE-627)SPR032087357 (SPR)s13373-015-0071-0-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE Ikoma, Norihisa verfasserin aut Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multi-dimensional case, we consider only radial eigenpairs. Our eigenvalue problem has a general first-order boundary condition which includes, as a special case, the Dirichlet, Neumann and Robin boundary conditions. Given a nonnegative integer n, we prove the existence and uniqueness, modulo multiplication of the eigenfunction by a positive constant, of an eigenpair whose eigenfunction, as a radial function in the multi-dimensional case, has exactly n zeroes. When an eigenfunction has n zeroes, we call the corresponding eigenvalue of nth order. Furthermore, we establish results concerning comparison of two eigenvalues, characterizations of nth order eigenvalues via differential inequalities, the maximum principle for the boundary value problem in connection with the principal eigenvalue, and existence of a solution having n zeroes, as a radial function in the multi-dimensional case, of the boundary value problem with an inhomogeneous term. Eigenvalue problem (dpeaa)DE-He213 Fully nonlinear equation (dpeaa)DE-He213 General boundary conditions (dpeaa)DE-He213 Principal eigenvalues (dpeaa)DE-He213 Higher order eigenvalues (dpeaa)DE-He213 Ishii, Hitoshi verfasserin aut Enthalten in Bulletin of mathematical sciences [Cham] : Springer International Publishing, 2011 5(2015), 3 vom: 25. Juli, Seite 451-510 (DE-627)654743967 (DE-600)2599335-5 1664-3615 nnns volume:5 year:2015 number:3 day:25 month:07 pages:451-510 https://dx.doi.org/10.1007/s13373-015-0071-0 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2015 3 25 07 451-510
language	English
source	Enthalten in Bulletin of mathematical sciences 5(2015), 3 vom: 25. Juli, Seite 451-510 volume:5 year:2015 number:3 day:25 month:07 pages:451-510
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topic_facet	Eigenvalue problem Fully nonlinear equation General boundary conditions Principal eigenvalues Higher order eigenvalues
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authorswithroles_txt_mv	Ikoma, Norihisa @@aut@@ Ishii, Hitoshi @@aut@@
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author	Ikoma, Norihisa
spellingShingle	Ikoma, Norihisa ddc 510 misc Eigenvalue problem misc Fully nonlinear equation misc General boundary conditions misc Principal eigenvalues misc Higher order eigenvalues Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II
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topic	ddc 510 misc Eigenvalue problem misc Fully nonlinear equation misc General boundary conditions misc Principal eigenvalues misc Higher order eigenvalues
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title	Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II
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title_full	Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II
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title_sort	eigenvalue problem for fully nonlinear second-order elliptic pde on balls, ii
title_auth	Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II
abstract	Abstract This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multi-dimensional case, we consider only radial eigenpairs. Our eigenvalue problem has a general first-order boundary condition which includes, as a special case, the Dirichlet, Neumann and Robin boundary conditions. Given a nonnegative integer n, we prove the existence and uniqueness, modulo multiplication of the eigenfunction by a positive constant, of an eigenpair whose eigenfunction, as a radial function in the multi-dimensional case, has exactly n zeroes. When an eigenfunction has n zeroes, we call the corresponding eigenvalue of nth order. Furthermore, we establish results concerning comparison of two eigenvalues, characterizations of nth order eigenvalues via differential inequalities, the maximum principle for the boundary value problem in connection with the principal eigenvalue, and existence of a solution having n zeroes, as a radial function in the multi-dimensional case, of the boundary value problem with an inhomogeneous term.
abstractGer	Abstract This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multi-dimensional case, we consider only radial eigenpairs. Our eigenvalue problem has a general first-order boundary condition which includes, as a special case, the Dirichlet, Neumann and Robin boundary conditions. Given a nonnegative integer n, we prove the existence and uniqueness, modulo multiplication of the eigenfunction by a positive constant, of an eigenpair whose eigenfunction, as a radial function in the multi-dimensional case, has exactly n zeroes. When an eigenfunction has n zeroes, we call the corresponding eigenvalue of nth order. Furthermore, we establish results concerning comparison of two eigenvalues, characterizations of nth order eigenvalues via differential inequalities, the maximum principle for the boundary value problem in connection with the principal eigenvalue, and existence of a solution having n zeroes, as a radial function in the multi-dimensional case, of the boundary value problem with an inhomogeneous term.
abstract_unstemmed	Abstract This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multi-dimensional case, we consider only radial eigenpairs. Our eigenvalue problem has a general first-order boundary condition which includes, as a special case, the Dirichlet, Neumann and Robin boundary conditions. Given a nonnegative integer n, we prove the existence and uniqueness, modulo multiplication of the eigenfunction by a positive constant, of an eigenpair whose eigenfunction, as a radial function in the multi-dimensional case, has exactly n zeroes. When an eigenfunction has n zeroes, we call the corresponding eigenvalue of nth order. Furthermore, we establish results concerning comparison of two eigenvalues, characterizations of nth order eigenvalues via differential inequalities, the maximum principle for the boundary value problem in connection with the principal eigenvalue, and existence of a solution having n zeroes, as a radial function in the multi-dimensional case, of the boundary value problem with an inhomogeneous term.
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title_short	Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II
url	https://dx.doi.org/10.1007/s13373-015-0071-0
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Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II

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