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

摘要

We prove the existence of a non-trivial weak solution for the equation by variational methods. We consider the case where a = λ_1 or b = λ_1, while the nonlinearity f belongs to a class that contains, for example, |u|~(q-2)u (1 < q < p).