# Existence Solution For Class Of P-laplacian Equations

Volume 4, Issue 1, pp 53 - 59 Publication Date: January 18, 2012
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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.

### Keywords

• p-laplacian
• weak solution
• homogenous.

### References

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