A priori bounds and multiplicity of solutions for an indefinite elliptic problem with critical growth in the gradient

Colette De Coster, Antonio J. Fernández, Louis Jeanjean

Let $\Omega \subset {\mathbb{R}}^N$, $N\ge 2$, be a smooth bounded domain. We consider a boundary value problem of the form $$-Δu = c_λ(x) u + μ(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(…