Existence results for Schrodinger-Choquard-Kirchhoff equations involving the fractional p-Laplacian

The paper is concerned with existence of nonnegative solutions of a Schrodinger-Choquard-Kirchhoff type fractional p-equation, involving critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. First, via th e Mountain Pass theorem, existence of nonnegative solutions is obtained when the nonlinearity f satisfies superlinear growth conditions and the involved real parameter is large enough. Then, via the Ekeland variational principle, existence of nonnegative solutions is investigated when f is sublinear at infinity and the real parameter is small enough. More intriguingly, the paper covers a novel feature of Kirchhoff problems, which is the fact that the Kitchhoff function M can be zero at zero, the so called degenerate case. Hence the results of the paper are new even for the standard stationary Kirchhoff problems.