The Fucík spectrum of the p-Laplacian and jumping nonlinear problems

We prove the existence of a nontrivial curve in the Fucík spectrum of the p-Laplacian using the sequence of minimax eigenvalues constructed by cohomological index. Furthermore, we study the solvability of jumping nonlinear problems:{−Δpu=α(u+)p−1−β(u−)p−1+f,x∈Ω,u=0,x∈∂Ω.