Infinite-dimensional homology and multibump solutions

  • Wojciech Kryszewski
  • Andrzej Szulkin


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.

Mathematics Subject Classification (2000).

Primary 58E05 Secondary 35Q55, 55N05, 58E30 


Čech homology infinite-dimensional homology critical group Schrödinger equation ground state solution multibump solution 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsNicholas Copernicus UniversityToruńPoland
  2. 2.Department of MathematicsStockholm UniversityStockholmSweden

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