Concentration phenomena and competition effects for fractional Kirchhoff-Choquard equations with exponential growth

Abstract

n this paper, we study the fractional Kirchhoff-Choquard equation where ε is a positive parameter, N = ps,p ≥ 2, s ∈ (0,1), 0 < μ < N. The Kirchhoff function M(t) = a + bt,a > 0,b > 0, nonlinear function f has the exponential growth, potential functions V and Q are continuous functions satisfying some suitable conditions. Using Ljusternik-Schnirelmann category theory and variational methods, we establish the multiplicity and concentration of positive solutions for small values of the parameter.