Existence and multiplicity results for a class of non-linear Schrödinger equations with magnetic potential involving sign-changing non linearity

Francisco Odair Vieira de Paiva, Sandra Machado de Souza Lima, Olimpio Hiroshi Miyagaki

In this work we consider the following class of elliptic problems $$- Δ_A u + u = a(x) |u|^{q-2}u+b(x) |u|^{p-2}u , \mbox{ in } \mathbb{R}^N, $$ $u\in H_A^1({\mathbb{R}}^N)$, with $…