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

Cabanillas Lapa, Eugenio and Barahona Martinez , Willy and Godoy Torres, Benigno and Rodriguez Varillas, Gabriel (2014) Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type. Armenian Journal of Mathematics, 6 (2). pp. 53-63. ISSN 1829-1163

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## Abstract

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.

Item Type: Article 35-xx Partial differential equations 593 Doctor Eugenio cabanillas Lapa 31 Jan 2015 16:24 02 Jul 2015 00:40

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