Dirichlet boundary value problem related to the p(x)-Laplacian with discontinuous nonlinearity
Abstract
In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to the p(x)-Laplacian -div(|∇ u|p(x)-2∇ u)+u∈ -[g(x,u),g(x,u)], by using the degree theory after turning the problem into a Hammerstein equation. The right hand side g is a possibly discontinuous function in the second variable satisfying some non-standard growth conditions..
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