A new infinite-dimensional linking theorem for parameter-dependent functionals and periodic Schrödinger equations

• DOI: 10.1016/j.jmaa.2015.06.041
• Publication Date: 2015-06-28T00:49:39Z
• Authors: Shaowei Chen; Lishan Lin; Liqin Xiao
• Keywords: Comparison theorem

Abstract We present a new infinite-dimensional linking theorem for parameter-dependent functionals. This theorem replaces some semi-continuous assumptions in the classical infinite-dimensional linking theorem with new assumptions and insures the existence of bounded and variant Palais–Smale sequences for a strongly indefinite functional. As an application of this theorem, we obtain nontrivial solutions for strongly indefinite periodic Schrodinger equations with sign-changing and asymptotically linear nonlinearities.