Periodic solutions of angiogenesis models with time lags

To enrich the dynamics of mathematical models of angiogenesis, all mechanisms involved are time-dependent. We also assume that the tumor cells enter the mechanisms of angiogenic stimulation and inhibition with some delays. The models under study belong to a special class of nonlinear nonautonomous s...

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Detalles Bibliográficos
Autores principales: Amster, P., Berezansky, L., Idels, L.
Formato: JOUR
Materias:
A priori estimates
Angiogenesis
Existence of positive periodic solutions
LeraySchauder degree methods
Nonlinear nonautonomous delay differential equations
Second order Liénard type equation
A-priori estimates
Nonautonomous
Second orders
Differential equations
Differentiation (calculus)
Mathematical models
Nonlinear equations
Problem solving
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_14681218_v13_n1_p299_Amster
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_14681218_v13_n1_p299_Amster
record_format dspace
spelling todo:paper_14681218_v13_n1_p299_Amster2023-10-03T16:17:26Z Periodic solutions of angiogenesis models with time lags Amster, P. Berezansky, L. Idels, L. A priori estimates Angiogenesis Existence of positive periodic solutions LeraySchauder degree methods Nonlinear nonautonomous delay differential equations Second order Liénard type equation A-priori estimates Angiogenesis Existence of positive periodic solutions LeraySchauder degree methods Nonautonomous Second orders Differential equations Differentiation (calculus) Mathematical models Nonlinear equations Problem solving To enrich the dynamics of mathematical models of angiogenesis, all mechanisms involved are time-dependent. We also assume that the tumor cells enter the mechanisms of angiogenic stimulation and inhibition with some delays. The models under study belong to a special class of nonlinear nonautonomous systems with delays. Explicit sufficient and necessary conditions for the existence of the positive periodic solutions were obtained via topological methods. Numerical examples illustrate our findings. Some open problems are presented for further studies. © 2011 Elsevier Ltd. All rights reserved. Fil:Amster, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_14681218_v13_n1_p299_Amster
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic A priori estimates
Angiogenesis
Existence of positive periodic solutions
LeraySchauder degree methods
Nonlinear nonautonomous delay differential equations
Second order Liénard type equation
A-priori estimates
Angiogenesis
Existence of positive periodic solutions
LeraySchauder degree methods
Nonautonomous
Second orders
Differential equations
Differentiation (calculus)
Mathematical models
Nonlinear equations
Problem solving
spellingShingle A priori estimates
Angiogenesis
Existence of positive periodic solutions
LeraySchauder degree methods
Nonlinear nonautonomous delay differential equations
Second order Liénard type equation
A-priori estimates
Angiogenesis
Existence of positive periodic solutions
LeraySchauder degree methods
Nonautonomous
Second orders
Differential equations
Differentiation (calculus)
Mathematical models
Nonlinear equations
Problem solving
Amster, P.
Berezansky, L.
Idels, L.
Periodic solutions of angiogenesis models with time lags
topic_facet A priori estimates
Angiogenesis
Existence of positive periodic solutions
LeraySchauder degree methods
Nonlinear nonautonomous delay differential equations
Second order Liénard type equation
A-priori estimates
Angiogenesis
Existence of positive periodic solutions
LeraySchauder degree methods
Nonautonomous
Second orders
Differential equations
Differentiation (calculus)
Mathematical models
Nonlinear equations
Problem solving
description To enrich the dynamics of mathematical models of angiogenesis, all mechanisms involved are time-dependent. We also assume that the tumor cells enter the mechanisms of angiogenic stimulation and inhibition with some delays. The models under study belong to a special class of nonlinear nonautonomous systems with delays. Explicit sufficient and necessary conditions for the existence of the positive periodic solutions were obtained via topological methods. Numerical examples illustrate our findings. Some open problems are presented for further studies. © 2011 Elsevier Ltd. All rights reserved.
format JOUR
author Amster, P.
Berezansky, L.
Idels, L.
author_facet Amster, P.
Berezansky, L.
Idels, L.
author_sort Amster, P.
title Periodic solutions of angiogenesis models with time lags
title_short Periodic solutions of angiogenesis models with time lags
title_full Periodic solutions of angiogenesis models with time lags
title_fullStr Periodic solutions of angiogenesis models with time lags
title_full_unstemmed Periodic solutions of angiogenesis models with time lags
title_sort periodic solutions of angiogenesis models with time lags
url http://hdl.handle.net/20.500.12110/paper_14681218_v13_n1_p299_Amster
work_keys_str_mv AT amsterp periodicsolutionsofangiogenesismodelswithtimelags
AT berezanskyl periodicsolutionsofangiogenesismodelswithtimelags
AT idelsl periodicsolutionsofangiogenesismodelswithtimelags
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