Infinitely Many Solutions for Schrodinger-Choquard Equation with Critical Exponential Growth in RN

In this work, we study the existence of infinitely many nonnegative solutions for Schrodinger-Choquard equation -Delta(N)u + V (x)vertical bar u vertical bar(N-2) u - Delta(N)(vertical bar u vertical bar(2 beta))vertical bar u vertical bar(2 beta-2) u = (I-alpha * vertical bar u vertical bar(q))vertical bar u vertical bar(q-2) u + h(u), x is an element of R-N, (0.1) where Delta(N) is the N-Laplacian operator, h(u) is odd and continuous function behaving likes exp(alpha(0)vertical bar u vertical bar N/N-1) when vertical bar u vertical bar -> infinity and N > 2 beta > 1. The potential V is an element of C(R-N) is positive and bounded in R-N. Using the Schwarz symmetrization with some special techniques and symmetric mountain pass lemma, we prove the existence of infinitely many solutions for (0.1) in W-1,W-N (R-N).