The existence of solutions, stability, and linearization of volterra systems

Abstract LetB be a Banach space ofRn valued continuous functions on [0, ∞) withf∈B. Consider the nonlinear Volterra integral equation (*)x(t)+ ∫otK(t,s,x(s))ds. We use the implicit function theorem to give sufficient conditions onB andK (t,s,x) for the existence of a unique solutionx∈B to (*) for ea...
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Gespeichert in:

Autor*in:	Ward, James R. [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	1977

Schlagwörter:	Banach Space Continuous Function Integral Equation Computational Mathematic Implicit Function Theorem

Systematik:	SA 6845 SA 6845

Anmerkung:	© Springer-Verlag New York Inc. 1977

Übergeordnetes Werk:	Enthalten in: Mathematical systems theory - Springer-Verlag, 1967, 11(1977), 1 vom: Dez., Seite 177-197
Übergeordnetes Werk:	volume:11 ; year:1977 ; number:1 ; month:12 ; pages:177-197

Links:	Volltext

DOI / URN:	10.1007/BF01768476

Katalog-ID:	OLC2061908896

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allfields	10.1007/BF01768476 doi (DE-627)OLC2061908896 (DE-He213)BF01768476-p DE-627 ger DE-627 rakwb eng 510 000 VZ SA 6845 VZ rvk SA 6845 VZ rvk Ward, James R. verfasserin aut The existence of solutions, stability, and linearization of volterra systems 1977 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc. 1977 Abstract LetB be a Banach space ofRn valued continuous functions on [0, ∞) withf∈B. Consider the nonlinear Volterra integral equation ()x(t)+ ∫otK(t,s,x(s))ds. We use the implicit function theorem to give sufficient conditions onB andK (t,s,x) for the existence of a unique solutionx∈B to () for eachf ∈B with ∥f∥B sufficiently small. Moreover, there is a constantM>0 independent off with ≤M∥f∥B. Banach Space Continuous Function Integral Equation Computational Mathematic Implicit Function Theorem Enthalten in Mathematical systems theory Springer-Verlag, 1967 11(1977), 1 vom: Dez., Seite 177-197 (DE-627)129081450 (DE-600)3459-9 (DE-576)014414325 0025-5661 nnns volume:11 year:1977 number:1 month:12 pages:177-197 https://doi.org/10.1007/BF01768476 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_60 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4266 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4316 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 SA 6845 SA 6845 AR 11 1977 1 12 177-197
spelling	10.1007/BF01768476 doi (DE-627)OLC2061908896 (DE-He213)BF01768476-p DE-627 ger DE-627 rakwb eng 510 000 VZ SA 6845 VZ rvk SA 6845 VZ rvk Ward, James R. verfasserin aut The existence of solutions, stability, and linearization of volterra systems 1977 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc. 1977 Abstract LetB be a Banach space ofRn valued continuous functions on [0, ∞) withf∈B. Consider the nonlinear Volterra integral equation ()x(t)+ ∫otK(t,s,x(s))ds. We use the implicit function theorem to give sufficient conditions onB andK (t,s,x) for the existence of a unique solutionx∈B to () for eachf ∈B with ∥f∥B sufficiently small. Moreover, there is a constantM>0 independent off with ≤M∥f∥B. Banach Space Continuous Function Integral Equation Computational Mathematic Implicit Function Theorem Enthalten in Mathematical systems theory Springer-Verlag, 1967 11(1977), 1 vom: Dez., Seite 177-197 (DE-627)129081450 (DE-600)3459-9 (DE-576)014414325 0025-5661 nnns volume:11 year:1977 number:1 month:12 pages:177-197 https://doi.org/10.1007/BF01768476 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_60 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4266 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4316 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 SA 6845 SA 6845 AR 11 1977 1 12 177-197
allfields_unstemmed	10.1007/BF01768476 doi (DE-627)OLC2061908896 (DE-He213)BF01768476-p DE-627 ger DE-627 rakwb eng 510 000 VZ SA 6845 VZ rvk SA 6845 VZ rvk Ward, James R. verfasserin aut The existence of solutions, stability, and linearization of volterra systems 1977 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc. 1977 Abstract LetB be a Banach space ofRn valued continuous functions on [0, ∞) withf∈B. Consider the nonlinear Volterra integral equation ()x(t)+ ∫otK(t,s,x(s))ds. We use the implicit function theorem to give sufficient conditions onB andK (t,s,x) for the existence of a unique solutionx∈B to () for eachf ∈B with ∥f∥B sufficiently small. Moreover, there is a constantM>0 independent off with ≤M∥f∥B. Banach Space Continuous Function Integral Equation Computational Mathematic Implicit Function Theorem Enthalten in Mathematical systems theory Springer-Verlag, 1967 11(1977), 1 vom: Dez., Seite 177-197 (DE-627)129081450 (DE-600)3459-9 (DE-576)014414325 0025-5661 nnns volume:11 year:1977 number:1 month:12 pages:177-197 https://doi.org/10.1007/BF01768476 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_60 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4266 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4316 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 SA 6845 SA 6845 AR 11 1977 1 12 177-197
allfieldsGer	10.1007/BF01768476 doi (DE-627)OLC2061908896 (DE-He213)BF01768476-p DE-627 ger DE-627 rakwb eng 510 000 VZ SA 6845 VZ rvk SA 6845 VZ rvk Ward, James R. verfasserin aut The existence of solutions, stability, and linearization of volterra systems 1977 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc. 1977 Abstract LetB be a Banach space ofRn valued continuous functions on [0, ∞) withf∈B. Consider the nonlinear Volterra integral equation ()x(t)+ ∫otK(t,s,x(s))ds. We use the implicit function theorem to give sufficient conditions onB andK (t,s,x) for the existence of a unique solutionx∈B to () for eachf ∈B with ∥f∥B sufficiently small. Moreover, there is a constantM>0 independent off with ≤M∥f∥B. Banach Space Continuous Function Integral Equation Computational Mathematic Implicit Function Theorem Enthalten in Mathematical systems theory Springer-Verlag, 1967 11(1977), 1 vom: Dez., Seite 177-197 (DE-627)129081450 (DE-600)3459-9 (DE-576)014414325 0025-5661 nnns volume:11 year:1977 number:1 month:12 pages:177-197 https://doi.org/10.1007/BF01768476 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_60 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4266 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4316 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 SA 6845 SA 6845 AR 11 1977 1 12 177-197
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author	Ward, James R.
spellingShingle	Ward, James R. ddc 510 rvk SA 6845 misc Banach Space misc Continuous Function misc Integral Equation misc Computational Mathematic misc Implicit Function Theorem The existence of solutions, stability, and linearization of volterra systems
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topic_title	510 000 VZ SA 6845 VZ rvk The existence of solutions, stability, and linearization of volterra systems Banach Space Continuous Function Integral Equation Computational Mathematic Implicit Function Theorem
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title	The existence of solutions, stability, and linearization of volterra systems
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title_full	The existence of solutions, stability, and linearization of volterra systems
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title_sort	the existence of solutions, stability, and linearization of volterra systems
title_auth	The existence of solutions, stability, and linearization of volterra systems
abstract	Abstract LetB be a Banach space ofRn valued continuous functions on [0, ∞) withf∈B. Consider the nonlinear Volterra integral equation ()x(t)+ ∫otK(t,s,x(s))ds. We use the implicit function theorem to give sufficient conditions onB andK (t,s,x) for the existence of a unique solutionx∈B to () for eachf ∈B with ∥f∥B sufficiently small. Moreover, there is a constantM>0 independent off with ≤M∥f∥B. © Springer-Verlag New York Inc. 1977
abstractGer	Abstract LetB be a Banach space ofRn valued continuous functions on [0, ∞) withf∈B. Consider the nonlinear Volterra integral equation ()x(t)+ ∫otK(t,s,x(s))ds. We use the implicit function theorem to give sufficient conditions onB andK (t,s,x) for the existence of a unique solutionx∈B to () for eachf ∈B with ∥f∥B sufficiently small. Moreover, there is a constantM>0 independent off with ≤M∥f∥B. © Springer-Verlag New York Inc. 1977
abstract_unstemmed	Abstract LetB be a Banach space ofRn valued continuous functions on [0, ∞) withf∈B. Consider the nonlinear Volterra integral equation ()x(t)+ ∫otK(t,s,x(s))ds. We use the implicit function theorem to give sufficient conditions onB andK (t,s,x) for the existence of a unique solutionx∈B to () for eachf ∈B with ∥f∥B sufficiently small. Moreover, there is a constantM>0 independent off with ≤M∥f∥B. © Springer-Verlag New York Inc. 1977
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title_short	The existence of solutions, stability, and linearization of volterra systems
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