JournalspmVol. 65, No. 4pp. 497–507

A remark on multiple solutions for a nonlinear eigenvalue problem

  • Gen-Qiang Wang

    Guangdong Polytechnic Normal University, Guangzhou, China
  • Sui Sun Cheng

    National Tsing Hua University, Hsinchu, Taiwan
A remark on multiple solutions for a nonlinear eigenvalue problem cover
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Abstract

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.

Cite this article

Gen-Qiang Wang, Sui Sun Cheng, A remark on multiple solutions for a nonlinear eigenvalue problem. Port. Math. 65 (2008), no. 4, pp. 497–507

DOI 10.4171/PM/1823