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

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 s...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2015-12, Vol.432 (1), p.233-253
Main Authors: Chen, Shaowei, Lin, Lishan, Xiao, Liqin
Format: Article
Language:English
Subjects:
Infinite-dimensional linking
Periodic Schrödinger equations
Sign-changing nonlinearities
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Summary: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 Schrödinger equations with sign-changing and asymptotically linear nonlinearities.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2015.06.041