New type of multi-bump solutions for Schrodinger-Poisson systems

In this article, we study the existence of non-radial positive solutions of the Schrodinger-Poisson system $$\displaylines{ -\Delta u+u+V(|x|)\Phi(x)u =Q(|x|) |u|^{p-1}u, \quad x\in \mathbb{R}^3, \cr -\Delta\Phi=V(|x|)u^2,\quad x\in \mathbb{R}^3, }$$ where \(1 < p< 5\) and $V, Q$ are radial potential functions. By developing some refined estimates, via the Lyapunov-Schmidt reduction method, we construct infinitely many multi-bump solutions when \(V, Q\) have some suitable algebraical decay at infinity. The maximum points of those multi-bump solutions are located on the top and bottom circles of a cylinder. This result not only gives a new type of multi-bump solutions but also extends the existence of multi-bump solutions to a general class of potential functions with a relatively slow decay rate at infinity. For more information see https://ejde.math.txstate.edu/Volumes/2025/72/abstr.html