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: ... where (-Δ)_p^s is the fractional p-Laplacian on the Heisenberg group ℍ^N, M is the Kirchhoff function, V (ξ) is the potential function, 0 < s < 1,1 < p < N/s, μ > 0, f (ξ, u) is the nonlinear function, 0 < λ < Q, Q = 2N + 2, and Q_λ* = 2Q-λ/Q-2 is the Sobolev critical exponent. Using the Krasnoselskii genus theorem, the existence of infinitely many solutions is obtained if μ is sufficiently large. In addition, using the fractional version of the concentrated compactness principle, we prove that problem has m pairs of solutions if μ is sufficiently small. As far as we know, the results of our study are new even in the Euclidean case. [ABSTRACT FROM AUTHOR]