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

Authors

  • Eugenio Cabanillas Lapa Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´
  • Willy Barahona Martinez Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´u
  • Benigno Godoy Torres Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´u
  • Gabriel Rodriguez Varillas Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´u

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.

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Published

2015-01-31

Issue

Vol. 6 No. 2 (2014)

Section

Articles

How to Cite

[1]
E. Cabanillas Lapa, W. Barahona Martinez, B. Godoy Torres, and G. Rodriguez Varillas, “Existence of Solutions for Semilinear Integro-differential Equations of p-Kirchhoff Type”, Armen.J.Math., vol. 6, no. 2, pp. 53–63, Jan. 2015, Accessed: Jan. 21, 2025. [Online]. Available: https://armjmath.sci.am/index.php/ajm/article/view/103