Existence of Weak Solutions for Weighted Robin Problem Involving p(.)-biharmonic operator

Abstract

Using Mountain Pass Theorem, we consider the existence of weak solutions of weighted Robin problem involving p(.)-biharmonic operator { a(x)Delta(2)(p(x)) u = lambda b(x)vertical bar u vertical bar(q(x)-2)u, in Omega a(x)vertical bar Delta u vertical bar(p(x)-2)partial derivative u/partial derivative v + beta(x) vertical bar u vertical bar(p(x)-2) u = 0, on partial derivative Omega under some conditions in the space W-a,b(2,p(.)) (Omega).