EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR CRITICAL KIRCHHOFF-CHOQUARD EQUATIONS INVOLVING THE FRACTIONAL p-LAPLACIAN ON THE HEISENBERG GROUP

In this paper, we study the existence and multiplicity of solutions for the following Kirchhoff-Choquard type equation involving the fractional p-Laplacian on the Heisenberg group:M(||u||(p)(mu))(mu(-Delta)(s)(p)u+V(xi)|u|(p-2)u) = f(xi,u)+integral N-H (|u(eta)|Q*)(lambda)/ (|eta-1 xi|)lambda d eta|u|Q* (-2)(lambda )u in H-N, where (Delta)(s)(p) is the fractional p-Laplacian on the Heisenberg group HN, M is the Kirchhoff function, V(xi) is the potential function, 0 < s < 1, 1 < p < (N)/(s) , mu > 0, f (xi,u) is the nonlinear function, 0 < lambda < Q, Q = 2N+2, and Q*(lambda)= (2Q-lambda)/( Q-2) is the Sobolev critical exponent. Using the Krasnoselskii genus theorem, the existence of infinitely many solutions is obtained if mu is sufficiently large. In addition, using the fractional version of the concentrated compactness principle, we prove that problem has m pairs of solutions if mu is sufficiently small. As far as we know, the results of our study are new even in the Euclidean case.