Concentrated solutions to fractional Schr\"{o}dinger-Poisson system with non-homogeneous potentials

TL;DR

This paper studies the existence, concentration, and uniqueness of normalized solutions to a fractional Schrödinger-Poisson system with non-homogeneous potentials, extending previous results in a more general nonlocal setting.

Contribution

It provides new existence and asymptotic results for solutions in a doubly nonlocal framework without assuming potential homogeneity, improving upon prior work.

Findings

Existence of normalized solutions established

Concentration behaviors characterized

Energy and decay estimates derived

Abstract

This paper mainly investigates several limit properties of normalized solutions for the fractional Schr\"{o}dinger-Poisson system, including existence, concentration behaviors and local uniqueness. It is worth noting that our results on the existence and asymptotic behaviors of normalized solutions are obtained in a doubly nonlocal setting and without assuming homogeneity of the potential, which generalize the results in \cite{GDCDS} in several aspects and improve our previous work in \cite{LIUYANG}. Meanwhile, some precise properties of solution sequence such as energy estimates, decay estimates and uniform regularity are also established by introducing some new techniques.