An infinite-dimensional linking theorem without upper semi-continuous assumption and its applications

• DOI: 10.1016/j.jmaa.2014.06.062
• Publication Date: 2014-06-26T15:16:28Z
• Authors: Shaowei Chen; Conglei Wang
• Keywords: Comparison theorem; Arzelà–Ascoli theorem; Existence theorem

Abstract We obtain a new infinite-dimensional linking theorem. This theorem replaces the upper semi-continuous assumption in the classical infinite-dimensional linking theorem of Kryszewski and Szulkin by a new assumption. As an application of this theorem, we obtain a nontrivial solution for a strongly indefinite periodic Schrodinger equation with sign-changing nonlinearity.