ArticleOriginal scientific text
Title
Nontrivial critical points of asymptotically quadratic functions at resonances
Authors 1
Affiliations
- Department of Mathematical Analysis, Faculty of Mathematics and Physics, Comenius University, Mlynská dolina, 842 15 Bratislava, Slovakia
Abstract
Asymptotically quadratic functions defined on Hilbert spaces are studied by using some results of the theory of Morse-Conley index. Applications are given to existence of nontrivial weak solutions for asymptotically linear elliptic partial and ordinary differential equations at resonances.
Keywords
weak solutions, boundary value problems, Morse-Conley index
Bibliography
- V. Benci, Some applications of the generalized Morse-Conley index, Confer. Semin. Mat. Univ. Bari 218 (1987).
- M. Fečkan, Critical points of asymptotically quadratic functions, Ann. Polon. Math. 61 (1995), 63-76.
- M. Fečkan, On a theorem of L. Lefton, Math. Slovaca 42 (1992), 195-200.
- L. Lefton, Existence of small solutions to a resonant boundary value problem with large nonlinearity, J. Differential Equations 85 (1990), 171-185.
- S. Li and J. Q. Liu, Morse theory and asymptotic linear Hamiltonian system, J. Differential Equations 78 (1989), 53-73.
- J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989.
- J. Nečas, Introduction to the Theory of Nonlinear Elliptic Equations, Teubner, Leipzig, 1983.
- B. Przeradzki, An abstract version of the resonance theorem, Ann. Polon. Math. 53 (1991), 35-43.
Pages:
43-57
Main language of publication
English
Received
1996-02-07
Published
1997
Exact and natural sciences