An infinite-dimensional linking theorem and applications
摘要
In this paper, we establish a new infinite-dimensional linking theorem without (PS)-type assumptions. The new theorem needs a weaker linking geometry and produces bounded (PS) sequences. The abstract result will be applied to the study of the existence of solutions of the strongly indefinite partial differential systems. For the first application, we consider the system Formula Not Shown where Ω is a bounded domain in RN with smooth boundary, is the outer normal derivative, H:∂Ω×R×R→R is a positive C1-function. One nontrivial solution is obtained. The second application, we will solve the eigenvalue problem of the system Formula Not Shown where A, B are self-adjoint operators on L2(Ω), Ω
RN is not necessarily bounded; f,g are Carathéodory functions on Ω×R2. We get infinitely many solutions. We deal with asymptotically linear cases for both systems.
RN is not necessarily bounded; f,g are Carathéodory functions on Ω×R2. We get infinitely many solutions. We deal with asymptotically linear cases for both systems.