p-Kirchhoff Modified Schrodinger Equation with Critical Nonlinearity in R^N

This article study the following on p-Kirchhoff modified Schrodinger equation with critical nonlinearity in R-N: kappa(u) + V (x)vertical bar u vertical bar(p-2) u = lambda (integral(RN) vertical bar u(y)vertical bar(2p mu)*/vertical bar y - x vertical bar(mu) dy)vertical bar u(x)vertical bar(2p mu)*(-2) u(x) +f(x, u)in R-N, where kappa(u) = - (a + b integral(RN) vertical bar del u vertical bar(p)dx) Delta(p)u - au Delta(p)(u(2)) with a > 0, b >= 0, 0 < mu < N, N >= 3, and lambda > 0 is a positive parameter. Here p(mu)* := p/2 2N-mu/N-p is the critical exponent with respect to the Hardy-Littlewood-Sobolev inequality. First, we establish the concentration-compactness principle related to our problem. Moreover, under some suitable assumptions on the nonlinearity f and the potential V, the existence of infinitely many nontrivial solutions are obtained by using the concentration-compactness principle and the symmetric mountain pass theorem. We generalize and fill in some of the previous results (Liang et al., Math Methods Appl Sci 43:2473-2490, 2020; Liang and Song, Differ Integral Equ 35:359-370, 2022; Yang and Ding, Ann Mat Pura Appl 192:783-804, 2013).