Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type
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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Republic of Armenia National Academy of Sciences
2015-01-01
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Series: | Armenian Journal of Mathematics |
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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.
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url |
http://www.armjmath.sci.am/index.php/ajm/article/view/103 |
work_keys_str_mv |
AT eugeniocabanillaslapa existenceofsolutionsforsemilinearintegrodifferentialequationsofpkirchhofftype AT willybarahonamartinez existenceofsolutionsforsemilinearintegrodifferentialequationsofpkirchhofftype AT benignogodoytorres existenceofsolutionsforsemilinearintegrodifferentialequationsofpkirchhofftype AT gabrielrodriguezvarillas existenceofsolutionsforsemilinearintegrodifferentialequationsofpkirchhofftype |
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1725415090590580736 |