# Nontrivial critical points of asymptotically quadratic functions at resonances

Annales Polonici Mathematici (1997)

- Volume: 67, Issue: 1, page 43-57
- ISSN: 0066-2216

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topMichal Fečkan. "Nontrivial critical points of asymptotically quadratic functions at resonances." Annales Polonici Mathematici 67.1 (1997): 43-57. <http://eudml.org/doc/270144>.

@article{MichalFečkan1997,

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.},

author = {Michal Fečkan},

journal = {Annales Polonici Mathematici},

keywords = {weak solutions; boundary value problems; Morse-Conley index; critical point theory; asymptotically linear differential equations; asymptotically quadratic functionals},

language = {eng},

number = {1},

pages = {43-57},

title = {Nontrivial critical points of asymptotically quadratic functions at resonances},

url = {http://eudml.org/doc/270144},

volume = {67},

year = {1997},

}

TY - JOUR

AU - Michal Fečkan

TI - Nontrivial critical points of asymptotically quadratic functions at resonances

JO - Annales Polonici Mathematici

PY - 1997

VL - 67

IS - 1

SP - 43

EP - 57

AB - 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.

LA - eng

KW - weak solutions; boundary value problems; Morse-Conley index; critical point theory; asymptotically linear differential equations; asymptotically quadratic functionals

UR - http://eudml.org/doc/270144

ER -

## References

top- [1] V. Benci, Some applications of the generalized Morse-Conley index, Confer. Semin. Mat. Univ. Bari 218 (1987). Zbl0656.58006
- [2] M. Fečkan, Critical points of asymptotically quadratic functions, Ann. Polon. Math. 61 (1995), 63-76. Zbl0820.58011
- [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. Zbl0699.34020
- [5] S. Li and J. Q. Liu, Morse theory and asymptotic linear Hamiltonian system, J. Differential Equations 78 (1989), 53-73. Zbl0672.34037
- [6] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989. Zbl0676.58017
- [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. Zbl0746.47043

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