The fractional Hartree equation without the Ambrosetti-Rabinowitz condition

TL;DR

This paper proves the existence of two non-trivial solutions for a class of fractional Hartree equations with general nonlinearities, without relying on the Ambrosetti-Rabinowitz condition, using variational methods.

Contribution

It introduces a novel approach to analyze fractional Hartree equations without the Ambrosetti-Rabinowitz condition, establishing the existence of positive and negative solutions.

Findings

Existence of two non-trivial solutions (positive and negative)

Solutions obtained without the Ambrosetti-Rabinowitz condition

Application of variational methods and critical point theory

Abstract

We consider a class of pseudo-relativistic Hartree equations in presence of general nonlinearities not satisfying the Ambrosetti-Rabinowitz condition. Using variational methods based on critical point theory, we show the existence of two non trivial signed solutions, one positive and one negative.