EXISTENCE SOLUTION FOR WEIGHTED p(x)-LAPLACIAN EQUATION, By Mohsen Alimohammady

Research

Title	EXISTENCE SOLUTION FOR WEIGHTED p(x)-LAPLACIAN EQUATION
Type	Article
Keywords	p(x)-biharmonic, variable exponent Lebesgue space, variable exponent Sobolev space
Journal	Italian Journal of Pure and Applied Mathematics
DOI	—
Researchers	S R MousavianKatir (First researcher) , Mohsen Alimohammady (Second researcher) , Hossein Jafari (Third researcher)

Abstract

This paper deals with the existence solution for the following type of boun- dary value problems: { Δ ( jxjp(x) jΔujp(x)􀀀2 Δu ) = jujq(x)􀀀2 u; in Ω; u = Δu = 0; on @Ω; where Ω is a smooth bounded domain in ℜN. It is established for a negative , there exists at least one weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces and a variant of the Mountain Pass theorem.