Existence Solution for Class of p-Laplacian Equations

Volume 4, Issue 1, pp 53--59 http://dx.doi.org/10.22436/jmcs.04.01.08

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Authors

Malihe Bagheri - Department of mathematic, Golestan Institute of Higher Education, Golestan Province, Iran Mahnaz Bagheri - Department of Mathematice, Islamic Azad University, behshar Branch, Iran

Abstract

We study existence of positive solution of the equation \[-\Delta_pu=\lambda|u|^{p-2}u+f(x,u)\] with zero Dirichlet boundary conditions in bounded domain \(\Omega\in \mathbb{R}^n\) where \(\Delta_p\) denotes the p-laplacian operator defined by \(-\Delta_pz=div(|\nabla z|^{p-2}\nabla z); p,\lambda\in \mathbb{R}\) and \(p>1\).Our main result establishes the existence of weak solution.

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Keywords

• p-laplacian
• weak solution
• homogenous.

MSC

•  35J66
•  35J92
•  35A01

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