Multiple solutions for an indefinite elliptic problem with critical growth in the gradient

Louis Jeanjean, Humberto Ramos Quoirin

We consider the problem $(P)$, $$-\Delta u=c(x)u+\mu |\nabla u{|}^2+f(x),u\in H_0^1(\Omega )\cap L^{\infty }(\Omega ),$$ where $\Omega$ is a bounded domain of ${\mathbb{R}}^N$, $N\ge 3$, $μ>0, \, c…