JournalspmVol. 65 , No. 4DOI 10.4171/pm/1823

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

A subscription is required to access this article.

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.