Multiplicity and concentration of solutions for fractional Kirchhoff–Choquard equation with critical growth

Abstract

In this paper, we are considered with class of fractional Kirchhoff–Choquard equation. Applying variational methods and topological arguments, we first investigate the existence of positive ground state solution and then consider relationship for the number of positive solutions and the topology of the set where the potential V attains its minimum. Finally, we give the concentrating behavior of solutions.

Multiple Normalized Solutions to a Choquard Equation Involving Fractional p-Laplacian in ℝN

“…For the supercritical growth case, Li and Wang [8] obtained the existence of a nontrivial solution to p-Laplacian equations in R N using the Moser iteration and perturbation arguments. For more interesting results, see [9][10][11][12] and their references.…”

“…When r = p, they showed that problem (12) has a ground-state solution with positive energy for c small enough. When r = 2, the authors also showed that problem (12) has at least two solutions, both with positive energy, where one is a ground state and the other is a high-energy solution.…”