Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System

We consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory.

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Main Authors: A. Gritsans, F. Sadyrbaev, I. Yermachenko
Format: Article
Language:English
Published: Wiley 2016-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2016/5676217
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author A. Gritsans
F. Sadyrbaev
I. Yermachenko
author_facet A. Gritsans
F. Sadyrbaev
I. Yermachenko
author_sort A. Gritsans
collection DOAJ
description We consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory.
format Article
id doaj-art-3f69144aef5746fe981a3e4144867586
institution Kabale University
issn 1687-9643
1687-9651
language English
publishDate 2016-01-01
publisher Wiley
record_format Article
series International Journal of Differential Equations
spelling doaj-art-3f69144aef5746fe981a3e41448675862025-08-20T03:35:51ZengWileyInternational Journal of Differential Equations1687-96431687-96512016-01-01201610.1155/2016/56762175676217Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear SystemA. Gritsans0F. Sadyrbaev1I. Yermachenko2Institute of Life Sciences and Technologies, Daugavpils University, Parades iela 1a, Daugavpils LV-5400, LatviaInstitute of Life Sciences and Technologies, Daugavpils University, Parades iela 1a, Daugavpils LV-5400, LatviaInstitute of Life Sciences and Technologies, Daugavpils University, Parades iela 1a, Daugavpils LV-5400, LatviaWe consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory.http://dx.doi.org/10.1155/2016/5676217
spellingShingle A. Gritsans
F. Sadyrbaev
I. Yermachenko
Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System
International Journal of Differential Equations
title Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System
title_full Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System
title_fullStr Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System
title_full_unstemmed Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System
title_short Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System
title_sort dirichlet boundary value problem for the second order asymptotically linear system
url http://dx.doi.org/10.1155/2016/5676217
work_keys_str_mv AT agritsans dirichletboundaryvalueproblemforthesecondorderasymptoticallylinearsystem
AT fsadyrbaev dirichletboundaryvalueproblemforthesecondorderasymptoticallylinearsystem
AT iyermachenko dirichletboundaryvalueproblemforthesecondorderasymptoticallylinearsystem