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Infinite-dimensional homology and multibump solutions
Department of Mathematics, Nicholas Copernicus University, Torun, Poland.
Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
2009 (English)In: Journal of Fixed Point Theory and Applications, ISSN 1661-7738, Vol. 5, no 1, 33 p.1-35 p.Article in journal (Refereed) Published
Abstract [en]

We start by introducing a Cech homology with compact supports which we then use in order to construct an infinite-dimensional homology theory. Next we show that under appropriate conditions on the nonlinearity there exists a ground state solution for a semilinear Schrödinger equation with strongly indefinite linear part. To this solution there corresponds a nontrivial critical group, defined in terms of the infinite-dimensional homology mentioned above. Finally we employ this fact in order to construct solutions of multibump type. Although our main purpose is to survey certain homological methods in critical point theory, we also include some new results.

Place, publisher, year, edition, pages
Basel: Birkhäuser , 2009. Vol. 5, no 1, 33 p.1-35 p.
Keyword [en]
Cech homology, infinite-dimensional homology, critical group, Schrödinger equation, ground state solution, multibump solution
National Category
Mathematical Analysis
Research subject
URN: urn:nbn:se:su:diva-16779DOI: 10.1007/s11784-009-0104-yISI: 000264548300001OAI: diva2:183299
Available from: 2008-12-23 Created: 2008-12-23 Last updated: 2010-01-04Bibliographically approved

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Szulkin, Andrzej
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ReferencesLink to record
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