Elliptic problems involving the -Laplacian with competing nonlinearities

By using the fibering method we study the existence of nonnegative solutions for the elliptic problem − Δ p ( x ) u = − λ a ( x ) | u | p ( x ) − 2 u + μ b ( x ) | u | q ( x ) − 2 u − ε c ( x ) | u | t ( x ) − 2 u in Ω , u = 0 on ∂ Ω , } where Ω ⊆ R N is a bounded domain, a ( . ) , b ( . ) , c ( . ) are essentially bounded functions and p ( . ) , q ( . ) , t ( . ) are continuous on Ω ¯ .