Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives

Abstract In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {Dq2u(t)=f(t,u(t),Dqu(t)),t∈I,Dqu(0)=0,Dqu(1)=αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder...
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Gespeichert in:

Autor*in:	Yu, Changlong [verfasserIn] Wang, Jufang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	-difference equations Leray-Schauder nonlinear alternative boundary value problem fixed point theorem

Übergeordnetes Werk:	Enthalten in: Advances in difference equations - [S.l.] : Springer International, 2004, 2013(2013), 1 vom: 02. Mai
Übergeordnetes Werk:	volume:2013 ; year:2013 ; number:1 ; day:02 ; month:05

Links:	Volltext

DOI / URN:	10.1186/1687-1847-2013-124

Katalog-ID:	SPR03289287X

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520			\|a Abstract In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {Dq2u(t)=f(t,u(t),Dqu(t)),t∈I,Dqu(0)=0,Dqu(1)=αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. The nonlinear team f contains in the equation.
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allfields	10.1186/1687-1847-2013-124 doi (DE-627)SPR03289287X (SPR)1687-1847-2013-124-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Yu, Changlong verfasserin aut Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {Dq2u(t)=f(t,u(t),Dqu(t)),t∈I,Dqu(0)=0,Dqu(1)=αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. The nonlinear team f contains in the equation. -difference equations (dpeaa)DE-He213 Leray-Schauder nonlinear alternative (dpeaa)DE-He213 boundary value problem (dpeaa)DE-He213 fixed point theorem (dpeaa)DE-He213 Wang, Jufang verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2013(2013), 1 vom: 02. Mai (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2013 year:2013 number:1 day:02 month:05 https://dx.doi.org/10.1186/1687-1847-2013-124 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 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 31.49 ASE AR 2013 2013 1 02 05
spelling	10.1186/1687-1847-2013-124 doi (DE-627)SPR03289287X (SPR)1687-1847-2013-124-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Yu, Changlong verfasserin aut Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {Dq2u(t)=f(t,u(t),Dqu(t)),t∈I,Dqu(0)=0,Dqu(1)=αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. The nonlinear team f contains in the equation. -difference equations (dpeaa)DE-He213 Leray-Schauder nonlinear alternative (dpeaa)DE-He213 boundary value problem (dpeaa)DE-He213 fixed point theorem (dpeaa)DE-He213 Wang, Jufang verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2013(2013), 1 vom: 02. Mai (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2013 year:2013 number:1 day:02 month:05 https://dx.doi.org/10.1186/1687-1847-2013-124 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 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 31.49 ASE AR 2013 2013 1 02 05
allfields_unstemmed	10.1186/1687-1847-2013-124 doi (DE-627)SPR03289287X (SPR)1687-1847-2013-124-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Yu, Changlong verfasserin aut Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {Dq2u(t)=f(t,u(t),Dqu(t)),t∈I,Dqu(0)=0,Dqu(1)=αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. The nonlinear team f contains in the equation. -difference equations (dpeaa)DE-He213 Leray-Schauder nonlinear alternative (dpeaa)DE-He213 boundary value problem (dpeaa)DE-He213 fixed point theorem (dpeaa)DE-He213 Wang, Jufang verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2013(2013), 1 vom: 02. Mai (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2013 year:2013 number:1 day:02 month:05 https://dx.doi.org/10.1186/1687-1847-2013-124 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 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 31.49 ASE AR 2013 2013 1 02 05
allfieldsGer	10.1186/1687-1847-2013-124 doi (DE-627)SPR03289287X (SPR)1687-1847-2013-124-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Yu, Changlong verfasserin aut Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {Dq2u(t)=f(t,u(t),Dqu(t)),t∈I,Dqu(0)=0,Dqu(1)=αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. The nonlinear team f contains in the equation. -difference equations (dpeaa)DE-He213 Leray-Schauder nonlinear alternative (dpeaa)DE-He213 boundary value problem (dpeaa)DE-He213 fixed point theorem (dpeaa)DE-He213 Wang, Jufang verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2013(2013), 1 vom: 02. Mai (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2013 year:2013 number:1 day:02 month:05 https://dx.doi.org/10.1186/1687-1847-2013-124 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 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 31.49 ASE AR 2013 2013 1 02 05
allfieldsSound	10.1186/1687-1847-2013-124 doi (DE-627)SPR03289287X (SPR)1687-1847-2013-124-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Yu, Changlong verfasserin aut Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {Dq2u(t)=f(t,u(t),Dqu(t)),t∈I,Dqu(0)=0,Dqu(1)=αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. The nonlinear team f contains in the equation. -difference equations (dpeaa)DE-He213 Leray-Schauder nonlinear alternative (dpeaa)DE-He213 boundary value problem (dpeaa)DE-He213 fixed point theorem (dpeaa)DE-He213 Wang, Jufang verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2013(2013), 1 vom: 02. Mai (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2013 year:2013 number:1 day:02 month:05 https://dx.doi.org/10.1186/1687-1847-2013-124 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 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 31.49 ASE AR 2013 2013 1 02 05
language	English
source	Enthalten in Advances in difference equations 2013(2013), 1 vom: 02. Mai volume:2013 year:2013 number:1 day:02 month:05
sourceStr	Enthalten in Advances in difference equations 2013(2013), 1 vom: 02. Mai volume:2013 year:2013 number:1 day:02 month:05
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	-difference equations Leray-Schauder nonlinear alternative boundary value problem fixed point theorem
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container_title	Advances in difference equations
authorswithroles_txt_mv	Yu, Changlong @@aut@@ Wang, Jufang @@aut@@
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author	Yu, Changlong
spellingShingle	Yu, Changlong ddc 510 bkl 31.49 misc -difference equations misc Leray-Schauder nonlinear alternative misc boundary value problem misc fixed point theorem Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives
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topic_title	510 610 ASE 31.49 bkl Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives -difference equations (dpeaa)DE-He213 Leray-Schauder nonlinear alternative (dpeaa)DE-He213 boundary value problem (dpeaa)DE-He213 fixed point theorem (dpeaa)DE-He213
topic	ddc 510 bkl 31.49 misc -difference equations misc Leray-Schauder nonlinear alternative misc boundary value problem misc fixed point theorem
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title	Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives
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title_full	Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives
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title_sort	existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives
title_auth	Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives
abstract	Abstract In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {Dq2u(t)=f(t,u(t),Dqu(t)),t∈I,Dqu(0)=0,Dqu(1)=αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. The nonlinear team f contains in the equation.
abstractGer	Abstract In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {Dq2u(t)=f(t,u(t),Dqu(t)),t∈I,Dqu(0)=0,Dqu(1)=αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. The nonlinear team f contains in the equation.
abstract_unstemmed	Abstract In this paper, we establish the existence of solutions for a boundary value problem with the nonlinear second-order q-difference equation {Dq2u(t)=f(t,u(t),Dqu(t)),t∈I,Dqu(0)=0,Dqu(1)=αu(1). The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. The nonlinear team f contains in the equation.
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title_short	Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives
url	https://dx.doi.org/10.1186/1687-1847-2013-124
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Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives

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