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Generalized Nehari manifold and semilinear Schrödinger equation with weak monotonicity condition on the nonlinear term
Stockholm University, Faculty of Science, Department of Mathematics.
2017 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 145, no 11, 4783-4794 p.Article in journal (Refereed) Published
Abstract [en]

We study the Schrodinger equations -Delta u + V (x) u = f( x, u) in R-N and -Delta u -lambda u = f( x, u) in a bounded domain Omega subset of R-N. We assume that f is superlinear but of subcritical growth and u bar right arrow f( x, u)/vertical bar u vertical bar is nondecreasing. In R-N we also assume that V and f are periodic in x1,..., xN. We show that these equations have a ground state and that there exist infinitely many solutions if f is odd in u. Our results generalize those by Szulkin and Weth [J. Funct. Anal. 257 (2009), 3802- 3822], where u bar right arrow f( x, u)/vertical bar u vertical bar was assumed to be strictly increasing. This seemingly small change forces us to go beyond methods of smooth analysis.

Place, publisher, year, edition, pages
2017. Vol. 145, no 11, 4783-4794 p.
Keyword [en]
Generalized Nehari manifold, Schrödinger equation, strongly indefinite functional, Clarke's subdifferential
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-134102DOI: 10.1090/proc/13609ISI: 000409193700019OAI: oai:DiVA.org:su-134102DiVA: diva2:1001159
Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2017-10-16Bibliographically approved

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