Critical superlinear Ambrosetti-Prodi problems

Abstract

We consider the existence of multiple solutions for problem (1.1) below with either $\lambda\neq \lambda$ or $\lambda=\lambda_1$, where $\lambda_k$, $k=1,2,\ldots$ are eigenvalues of $(-\Delta, H^1_0(\Omega))$. The local bifurcation from $\lambda=\lambda_k$ is also investigated.