Multiplicity and Concentration Results for Some Fractional Double Phase Choquard Equation with Exponential Growth

In this paper, we study the fractional Choquard equation in R-N epsilon(ps)(-Delta)(p)(s)u+epsilon(qs)(-Delta)(q)(s)u+V(x)(|u|(p-2)u+|u|q-2u)=epsilon(mu-N)[|x|(-mu)*F(u)]f(u), where epsilon is a positive parameter, N=ps,2 <= p<q,s is an element of(0,1),0<mu<N. The nonlinear function f has an exponential growth at infinity and the potential function V is continuous in RN and satisfies suitable natural conditions. Using the Ljusternik-Schnirelmann category theory and variational methods, we establish multiplicity and concentration of positive solutions for small values of the parameter epsilon>0.