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  1. Journal of Fixed Point Theory and Applications
  2. Journal of Fixed Point Theory and Applications : Volume 5
  3. Journal of Fixed Point Theory and Applications : Volume 5, Issue 1, March 2009
  4. Infinite-dimensional homology and multibump solutions
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Journal of Fixed Point Theory and Applications : Volume 19
Journal of Fixed Point Theory and Applications : Volume 18
Journal of Fixed Point Theory and Applications : Volume 17
Journal of Fixed Point Theory and Applications : Volume 16
Journal of Fixed Point Theory and Applications : Volume 15
Journal of Fixed Point Theory and Applications : Volume 14
Journal of Fixed Point Theory and Applications : Volume 13
Journal of Fixed Point Theory and Applications : Volume 12
Journal of Fixed Point Theory and Applications : Volume 11
Journal of Fixed Point Theory and Applications : Volume 10
Journal of Fixed Point Theory and Applications : Volume 9
Journal of Fixed Point Theory and Applications : Volume 8
Journal of Fixed Point Theory and Applications : Volume 7
Journal of Fixed Point Theory and Applications : Volume 6
Journal of Fixed Point Theory and Applications : Volume 5
Journal of Fixed Point Theory and Applications : Volume 5, Issue 2, August 2009
Journal of Fixed Point Theory and Applications : Volume 5, Issue 1, March 2009
Infinite-dimensional homology and multibump solutions
Remarks on u$_{0}$-positive operators
Around Browder’s fixed point theorem for contractions
Linear fractional mappings: invariant sets, semigroups and commutativity
Strong convergence of Browder’s type iterations for left amenable semigroups of Lipschitzian mappings in Banach spaces
Locally covering maps in metric spaces and coincidence points
L$^{p}$ theory for semilinear nonlocal problems with measure of noncompactness in separable Banach spaces
Systems of sandwich pairs
Pairs of positive solutions for the periodic scalar p-Laplacian
On some variational properties of metric spaces
Journal of Fixed Point Theory and Applications : Volume 4
Journal of Fixed Point Theory and Applications : Volume 3
Journal of Fixed Point Theory and Applications : Volume 2
Journal of Fixed Point Theory and Applications : Volume 1

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Infinite-dimensional homology and multibump solutions

Content Provider Springer Nature Link
Author Kryszewski, Wojciech Szulkin, Andrzej
Copyright Year 2009
Abstract We start by introducing a Čech 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.
Starting Page 1
Ending Page 35
Page Count 35
File Format PDF
ISSN 16617738
Journal Journal of Fixed Point Theory and Applications
Volume Number 5
Issue Number 1
e-ISSN 16617746
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2009-01-01
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Čech homology infinite-dimensional homology critical group Schrödinger equation ground state solution multibump solution Abstract critical point theory NLS-like equations Čech types Variational principles Mathematics Analysis Mathematical Methods in Physics
Content Type Text
Resource Type Article
Subject Geometry and Topology Applied Mathematics Modeling and Simulation
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