Concentrated solutions to fractional Schrödinger-Poisson system with non-homogeneous potentials

Abstract

This paper mainly investigates several limit properties of normalized solutions for the fractional Schrödinger-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.

Theorems & Definitions (34)

• Theorem 1.1
• Remark 1.2
• Theorem 1.3
• Theorem 1.4
• Remark 1.5
• Lemma 2.1
• proof
• Proposition 2.2
• proof
• proof : Proof of Theorem \ref{['the1']}