Infinitely many sign-changing solutions for p-Laplacian equation involving the critical Sobolev exponent
Department of Mathematics, Soochow University, Suzhou, Jiangsu, 215006, P.R. China
Boundary Value Problems 2013, 2013:149 doi:10.1186/1687-2770-2013-149Published: 19 June 2013
In this paper, we study the following problem:
where is a smooth bounded domain, , is the p-Laplacian, is the critical Sobolev exponent and is a parameter. By establishing a new deformation lemma, we show that if , then for each , 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).