Existence of infinitely many solutions for degenerate p-fractional Kirchhoff equations with critical Sobolev-Hardy nonlinearities

In this paper, we study a class of degenerate p-fractional Kirchhoff equations with critical Hardy-Sobolev nonlinearities M (integral integral(R2N) vertical bar u(x) - u(y)vertical bar(p)/vertical bar x - y vertical bar(N+ps) dxdy) (-Delta)(p)(s)u = lambda w(x)vertical bar u vertical bar(q-2)u + vertical bar u vertical bar(ps)*((alpha)-2)u/vertical bar x vertical bar(alpha), x is an element of R-N, where (-Delta)(p)(s) is the fractional p-Laplacian operator with 0 < s < 1 < p < infinity, dimension N > ps, 1 < q < p(s)*(alpha), p(s)*(alpha) = p(N - alpha)/(N - ps) is the critical exponent of the fractional Hardy-Sobolev exponent with alpha is an element of [0, ps), lambda is a positive parameter, M is a nonnegative function, while w is a positive weight. By means of the Kajikiya's new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions which tend to zero under a suitable value of lambda. The main feature and difficulty of our equations is the fact that the Kirchhoff term M could be zero at zero, that is the equation is degenerate. To our best knowledge, our results are new even in the Laplacian and p-Laplacian cases.