On the noncooperative Schrödinger–Kirchhoff system involving the critical nonlinearities on the Heisenberg group

Abstract

Abstract This paper deals with the existence of solutions for the noncooperative Schrödinger–Kirchhoff system involving the p-Laplacian operator and critical nonlinearities on the Heisenberg group. Under some suitable conditions, together with the limit index theory and the concentration–compactness principle, we obtain the existence and multiplicity of solutions for this system. To our best knowledge, the existence results for the noncooperative system with p-Laplacian and critical nonlinearities are new on the Heisenberg group.

Keywords

• Heisenberg group
• Schrödinger–Kirchhoff system
• p-Laplacian operator
• Limit index theory
• Critical Sobolev exponent