Existence of entire solutions for critical Sobolev–Hardy problems involving magnetic fractional operator

Abstract

In this paper, we deal with a class of Schrödinger–Kirchhoff problems in , driven by the fractional magnetic operator, involving critical Sobolev–Hardy nonlinearities and a nontrivial perturbation term. By variational approach, we obtain the existence of solutions which tend to zero under a suitable value of λ. The main feature and difficulty of our equations is the presence of the magnetic field and critical term as well as the possible degenerate nature of the Kirchhoff function M.