Nontrivial critical points of asymptotically quadratic functions at resonances

• Autorzy: Michal Fečkan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

weak solutions   boundary value problems   Morse-Conley index  

Kategorie tematyczne

• 34B15: Nonlinear boundary value problems
• 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel\cprime man) theory, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 67
• Numer: 1
• Strony: 43-57

Daty

wydano

1997

otrzymano

1996-02-07

Twórcy

autor

Michal Fečkan

• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Comenius University, Mlynská dolina, 842 15 Bratislava, Slovakia

Bibliografia

• [1] V. Benci, Some applications of the generalized Morse-Conley index, Confer. Semin. Mat. Univ. Bari 218 (1987).
• [2] M. Fečkan, Critical points of asymptotically quadratic functions, Ann. Polon. Math. 61 (1995), 63-76.
• [3] M. Fečkan, On a theorem of L. Lefton, Math. Slovaca 42 (1992), 195-200.
• [4] L. Lefton, Existence of small solutions to a resonant boundary value problem with large nonlinearity, J. Differential Equations 85 (1990), 171-185.
• [5] S. Li and J. Q. Liu, Morse theory and asymptotic linear Hamiltonian system, J. Differential Equations 78 (1989), 53-73.
• [6] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989.
• [7] J. Nečas, Introduction to the Theory of Nonlinear Elliptic Equations, Teubner, Leipzig, 1983.
• [8] B. Przeradzki, An abstract version of the resonance theorem, Ann. Polon. Math. 53 (1991), 35-43.