Nontrivial solutions for periodic Schr\"odinger equations with sign-changing nonlinearities
Shaowei Chen, Conglei Wang, Liqin Xiao
TL;DR
This paper introduces a novel mathematical approach to find nontrivial solutions for complex periodic Schr"odinger equations with nonlinearities that change sign, expanding the understanding of such quantum systems.
Contribution
It develops a new infinite-dimensional linking theorem to address strongly indefinite problems with sign-changing nonlinearities in Schr"odinger equations.
Findings
Established existence of nontrivial solutions for the equations.
Extended mathematical tools for indefinite and sign-changing nonlinear problems.
Provided a framework applicable to complex quantum systems.
Abstract
Using a new infinite-dimensional linking theorem, we obtained nontrivial solutions for strongly indefinite periodic Schr\"odinger equations with sign-changing nonlinearities.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Photonic Systems · Spectral Theory in Mathematical Physics