Elliptic problems involving the p(x)-Laplacian with competing nonlinearities

By using the fibering method we study the existence of nonnegative solutions for the elliptic problem−Δp(x)u=−λa(x)|u|p(x)−2u+μb(x)|u|q(x)−2u−εc(x)|u|t(x)−2uin Ω,u=0on ∂Ω,}where Ω⊆RN is a bounded domain, a(.), b(.), c(.) are essentially bounded functions and p(.), q(.), t(.) are continuous on Ω¯.