Existence and multiplicity results for a class of non-linear Schr\"odinger equations with magnetic potential involving sign-changing non linearity
In this work we consider the following class of elliptic problems $$- \Delta_A u + u = a(x) |u|^{q-2}u+b(x) |u|^{p-2}u , \mbox{ in } \mathbb{R}^N, $$ $u\in H^1_A (\mathbb{R}^N)$, with $2<q<p<2^*= \frac{2N}{N-2}$, $a(x)$ and $b(x)$ are functions that can change signal and satisfy some additional conditions; $u \in H^1_A(\mathbb{R}^N)$ and $A:\mathbb{R}^N \rightarrow \mathbb{R}^N$ is a magnetic potential. Also using the Nehari method in combination with other complementary arguments, we discuss the existence of infinite solutions to the problem in question, varying the assumptions about the weight functions.
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Analysis of PDEs
