Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type

Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type

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In our research we will study the existence of weak solutions to the problem $$ -[M(\|u\|^{p}_{1,p})]^{p-1}\Delta_{p} u = f(x,u)+\int_{\Omega}k(x,y)H(u)dy \quad \mbox{in }\Omega,$$ \noindent with zero Dirichlet boundary condition on a bounded smooth domain of $\mathbb{R}^{n} $, $ $ $1<p<N$; $...

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Main Authors: Eugenio Cabanillas Lapa, Willy Barahona Martinez, Benigno Godoy Torres, Gabriel Rodriguez Varillas
Format: Article
Language:English
Published: Republic of Armenia National Academy of Sciences 2015-01-01
Series:Armenian Journal of Mathematics
Online Access:http://www.armjmath.sci.am/index.php/ajm/article/view/103
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spelling doaj-73ab974587714c35aee1094bb3789a1d2020-11-25T00:08:40ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632015-01-0162Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff TypeEugenio Cabanillas Lapa0Willy Barahona Martinez1Benigno Godoy Torres2Gabriel Rodriguez Varillas3Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´uInstituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´uInstituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´u In our research we will study the existence of weak solutions to the problem $$ -[M(\|u\|^{p}_{1,p})]^{p-1}\Delta_{p} u = f(x,u)+\int_{\Omega}k(x,y)H(u)dy \quad \mbox{in }\Omega,$$ \noindent with zero Dirichlet boundary condition on a bounded smooth domain of $\mathbb{R}^{n} $, $ $ $1<p<N$; $M$,$f$,$k$ and $H$ are given functions. By means of the Galerkin method and using of the Brouwer Fixed Point theorem we get our results. The uniqueness of a weak solution is also considered. http://www.armjmath.sci.am/index.php/ajm/article/view/103
collection DOAJ
language English
format Article
sources DOAJ
author Eugenio Cabanillas Lapa
Willy Barahona Martinez
Benigno Godoy Torres
Gabriel Rodriguez Varillas
spellingShingle Eugenio Cabanillas Lapa
Willy Barahona Martinez
Benigno Godoy Torres
Gabriel Rodriguez Varillas
Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type
Armenian Journal of Mathematics
author_facet Eugenio Cabanillas Lapa
Willy Barahona Martinez
Benigno Godoy Torres
Gabriel Rodriguez Varillas
author_sort Eugenio Cabanillas Lapa
title Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type
title_short Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type
title_full Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type
title_fullStr Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type
title_full_unstemmed Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type
title_sort existence of solutions for semilinear integro-differential equations of p-kirchhoff type
publisher Republic of Armenia National Academy of Sciences
series Armenian Journal of Mathematics
issn 1829-1163
publishDate 2015-01-01
description In our research we will study the existence of weak solutions to the problem $$ -[M(\|u\|^{p}_{1,p})]^{p-1}\Delta_{p} u = f(x,u)+\int_{\Omega}k(x,y)H(u)dy \quad \mbox{in }\Omega,$$ \noindent with zero Dirichlet boundary condition on a bounded smooth domain of $\mathbb{R}^{n} $, $ $ $1<p<N$; $M$,$f$,$k$ and $H$ are given functions. By means of the Galerkin method and using of the Brouwer Fixed Point theorem we get our results. The uniqueness of a weak solution is also considered.
url http://www.armjmath.sci.am/index.php/ajm/article/view/103
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AT willybarahonamartinez existenceofsolutionsforsemilinearintegrodifferentialequationsofpkirchhofftype
AT benignogodoytorres existenceofsolutionsforsemilinearintegrodifferentialequationsofpkirchhofftype
AT gabrielrodriguezvarillas existenceofsolutionsforsemilinearintegrodifferentialequationsofpkirchhofftype
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