MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR FRACTIONAL MAGNETIC SCHRÖDINGER-POISSON EQUATION

In this paper, we consider the following fractional Schrödinger-Poisson equation with magnetic fields <p class="disp_formula">$\varepsilon^{2 s}(-\Delta)_{A / \varepsilon}^s u+V(x) u+\varepsilon^{-2}\left(|x|^{-1} *|u|^2\right) u=f\left(|u|^2\right) u \quad \text { in } \mathbb{R}^3,$ where <i>ε</i> &gt; 0 is a small parameter, <i>V</i>(<i>x</i>) : <i>R</i>³ → <i>R</i> and <i>A</i>(<i>x</i>) : <i>R</i>³ → <i>R</i>³ are continuous potentials. Under a local assumption on the potential <i>V</i>, by variational methods, penalization technique and Ljusternik-Schnirelmann theory, we obtain the multiplicity and concentration phenomena of nontrivial solutions of the above problem for <i>ε</i> &gt; 0 small. In this problem, the function <i>f</i> is only continuous, which allow to consider larger classes of nonlinearities in the reaction.