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.