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 Multiple periodic solutions for eigenvalue problems with a $p$-Laplacian and non-smooth potential Bull. Korean Math. Soc. 2011 Vol. 48, No. 1, 213-221 https://doi.org/10.4134/BKMS.2011.48.1.213Printed January 1, 2011 Guoqing Zhang and Sanyang Liu University of Shanghai for Science and Technology, Xidian University Abstract : In this paper, we establish a multiple critical points theorem for a one-parameter family of non-smooth functionals. The obtained result is then exploited to prove a multiplicity result for a class of periodic eigenvalue problems driven by the $p$-Laplacian and with a non-smooth potential. Under suitable assumptions, we locate an open subinterval of the eigenvalue. Keywords : multiple periodic solutions, critical points of non-smooth functionals, eigenvalue problems, $p$-Laplacian MSC numbers : 34C25 Downloads: Full-text PDF