Infinitely many sign-changing solutions for p-Laplacian equation involving the critical Sobolev exponent

In this paper, we study the following problem: {-Delta(p)u = lambda vertical bar u vertical bar(p2)u + vertical bar u vertical bar(p*) (2)u in Omega, u=0 on partial derivative Omega, where Omega subset of R-N is a smooth bounded domain, 1 < p < N, -Delta(p)u = div(vertical bar del u vertical bar(p-2)del u, is the p-Laplacian, p* = pN/(N-p) is the critical Sobolev exponent and lambda > 0 is a parameter. By establishing a new deformation lemma, we show that if N > p(2)+p, then for each lambda=0, this problem has infinitely many sign-changing solutions, which extends the results obtained in (Cao et al. in J. Funct. Anal. 262: 2861-2902, 2012; Schechter and Zou in Arch. Ration. Mech. Anal. 197: 337-356, 2010).