A generalized Fucik type eigenvalue problem for p-Laplacian

Abstract

In this paper we study the generalized Fucik type eigenvalue for the boundary value problem of one dimensional $p-$Laplace type differential equations -(φ(u'))' = ψ(u), u(-T) = u(T) =0, where φ(s) = α s^p, ψ(s)= λs^p, s >0; φ(s) = -β|s|^p, ψ(s)= -μ|s|^p, s <0. We say (α, β, λ, μ) belong to the Fucik spectrum, if the above boundary value problem has a non-trival solution. We have obtained a complete and explicit characterization of Fucik spectrum for such problem.