Multiple Solutions for a Class of Generalized Critical Noncooperative Schr & oacute;dinger Systems in R-N

In this paper, we investigate the multiplicity of solutions for a class of noncooperative Schr & ouml;dinger systems in R-N. The systems involves a variable exponent elliptic operators with critical nonlinearity. By applying the Limit Index Theory developed by Li (Nonlinear Anal 25, 1371-1389, 1995) and utilizing a version of the concentration-compactness principle and the principle of symmetric criticality of Krawcewicz and Marzantowicz, we obtain a sequence of solutions under appropriate assumptions.