Generalized Nehari manifold and semilinear Schrödinger equation with weak monotonicity condition on the nonlinear term

Francisco Odair de Paiva, Wojciech Kryszewski, Andrzej Szulkin

We study the Schrödinger equations $-\Delta u+V(x)u=f(x,u)$ in ${\mathbb{R}}^N$ and $-\Delta u-\lambda u=f(x,u)$ in a bounded domain $\Omega \subset {\mathbb{R}}^N$. We assume that $f$ is superlinear bu…