SCHRODINGER-KIRCHHOFF-HARDY p-RACTIONAL EQUATIONS WITHOUT THE AMBROSETTI-RABINOWITZ CONDITION

This paper is devoted to the study of the following Schrodinger-Kirchhoff-Hardy equation in R-n M(integral integral(R2n) vertical bar u(x) - u(y)vertical bar(p)/vertical bar x - y vertical bar(n) vertical bar ps dxdy) (-Delta)(p)(s)u + V(x)vertical bar u vertical bar(p-2) u-u vertical bar u vertical bar(p-2)u/vertical bar x vertical bar p(s) = f(x, u), where (-Delta)(p)(s) is the fractional p-Laplacian, with s is an element of (0, 1) and p > 1, dimension n > ps, M models a Kirchhoff coefficient, V is a positive potential, f is a continuous nonlinearity and mu is a real parameter. The main feature of the paper is the combination of a Kirchhoff coefficient and a Hardy term with a suitable function f which does not necessarily satisfy the Ambrosetti-Rabinowitz condition. Under different assumptions for f and restrictions for mu, we provide existence and multiplicity results by variational methods.