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Portugaliae Mathematica


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Volume 65, Issue 4, 2008, pp. 497–507
DOI: 10.4171/PM/1823

Published online: 2008-12-31

A remark on multiple solutions for a nonlinear eigenvalue problem

Gen-Qiang Wang[1] and Sui Sun Cheng[2]

(1) Guangdong Polytechnic Normal University, Guangzhou, China
(2) National Tsing Hua University, Hsinchu, Taiwan

Multiple solutions are shown to exist for the system Bu = λF(u), where λ > 0, B is a positive definite matrix and F is ‘superquadratic’ or ‘subquadratic’. We make use of Clark's theorem in critical point theory to obtain our results and provide examples to show that the results are sharp.

Keywords: Nonlinear system, steady state, Clark's theorem, critical point

Wang Gen-Qiang, Cheng Sui Sun: A remark on multiple solutions for a nonlinear eigenvalue problem. Port. Math. 65 (2008), 497-507. doi: 10.4171/PM/1823