On some weakly coercive quasilinear problems with forcing

Andrzej Szulkin, Michel Willem

We consider the forced problem $-{\Delta }_{p}u-V(x)|u{|}^{p-2}u=f(x)$, where ${\Delta }_p$ is the $p$-Laplacian ($1<p<\infty$) in a domain $\Omega \subset {\mathbb{R}}^N$, $V\ge 0$ and $Q_V (u) := \int…