Existence of a non-trivial solution for the p-Laplacian equation with Fučík type resonance at infinity

We prove the existence of a non-trivial weak solution for the equation {−Δpu=au+p−1−bu−p−1+f(x,u)inΩ,u=0on∂Ω, by variational methods. We consider the case where a=λ1a=λ1 or b=λ1b=λ1, while the nonlinearity ff belongs to a class that contains, for example, |u|q−2u|u|q−2u (1