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Bull. Korean Math. Soc. 2013; 50(1): 57-71

Printed January 31, 2013

https://doi.org/10.4134/BKMS.2013.50.1.57

Copyright © The Korean Mathematical Society.

Existence of three solutions for a class of Navier quasilinear elliptic systems involving the $(p_1,\ldots,p_n)$-biharmonic

Lin Li

Sichuan University of Science and Engineering

Abstract

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In this paper, we establish the existence of at least three solutions to a Navier boundary problem involving the $(p_1,\ldots,p_n)$-biharmonic systems. We use a variational approach based on a three critical points theorem due to Ricceri [B. Ricceri, {\it A three critical points theorem revisited}, Nonlinear Anal. {\bf 70} (2009), 3084--3089].

Keywords: $(p_1,\ldots,p_n)$-biharmonic, Navier condition, multiple solutions, three critical points theorem

MSC numbers: 35J48, 35J60, 47J30, 58E05

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