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Bull. Korean Math. Soc. 2011; 48(1): 213-221
Printed January 1, 2011
https://doi.org/10.4134/BKMS.2011.48.1.213
Copyright © The Korean Mathematical Society.
Multiple periodic solutions for eigenvalue problems with a $p$-Laplacian and non-smooth potential
Guoqing Zhang and Sanyang Liu
University of Shanghai for Science and Technology, Xidian University
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
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