Existence results for non-coercive problems - Diblík Josef; Galewski Marek; Šmarda Zdenĕk (Advances in Nonlinear Analysis)
In this article, we investigate non-coercive variational equations under assumptions related to generalized monotonicity. We present some general abstract tools regarding the existence of bounded solutions and their multiplicity, which we then apply to the Dirichlet boundary value problem driven by the perturbed (negative) pp-Laplacian. As a by-product of our findings, we provide a version of the Browder-Minty theorem in the potential case that does not involve the Brouwer fixed-point theorem but utilizes optimization techniques.