Nontrivial critical points of asymptotically quadratic functions at resonances

Michal Fečkan

Annales Polonici Mathematici (1997)

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

Abstract

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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.

How to cite

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Michal 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

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  1. [1] V. Benci, Some applications of the generalized Morse-Conley index, Confer. Semin. Mat. Univ. Bari 218 (1987). Zbl0656.58006
  2. [2] M. Fečkan, Critical points of asymptotically quadratic functions, Ann. Polon. Math. 61 (1995), 63-76. Zbl0820.58011
  3. [3] M. Fečkan, On a theorem of L. Lefton, Math. Slovaca 42 (1992), 195-200. 
  4. [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. [5] S. Li and J. Q. Liu, Morse theory and asymptotic linear Hamiltonian system, J. Differential Equations 78 (1989), 53-73. Zbl0672.34037
  6. [6] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989. Zbl0676.58017
  7. [7] J. Nečas, Introduction to the Theory of Nonlinear Elliptic Equations, Teubner, Leipzig, 1983. 
  8. [8] B. Przeradzki, An abstract version of the resonance theorem, Ann. Polon. Math. 53 (1991), 35-43. Zbl0746.47043

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