Critical groups at infinity for p-Laplacian equations with indefinite nonlinearities

In this paper, by a kind of decomposition lemma and Künneth formula we study the critical groups at infinity for the associated functional of the following p-Laplacian equation with indefinite nonlinearities{−Δpu=λ|u|p−2u+a+(x)f(u)−a−(x)|u|q−2u+h(x,u)in Ω,u=0on ∂Ω. We also obtain the existence of multiple nontrivial solutions of this equation via Morse theory.