Existence Solution for Class of p-Laplacian Equations


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.


Keywords


MSC


References