A remark on multiple solutions for a nonlinear eigenvalue problem

Abstract

Multiple solutions are shown to exist for the system $Bu=\lambda F(u)$, where $\lambda >0$, $B$ 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.