Multiple solutions for noncooperative -Laplacian equations in involving the critical exponent

In this paper, we study the multiplicity of solutions for a class of noncooperative p ( x ) -Laplacian equations in R N involving the critical exponent. By using the Limit Index Theory due to Li [Y.Q. Li, A limit index theory and its application, Nonlinear Anal. 25 (1995) 1371–1389] and concentration-compactness principle, we obtain a sequence of radially symmetric solutions.