A critical point result for non-differentiable indefinite functionals

Salvatore A. Marano; Dumitru Motreanu

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 4, page 663-679
  • ISSN: 0010-2628

Abstract

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In this paper, two deformation lemmas concerning a family of indefinite, non necessarily continuously differentiable functionals are proved. A critical point theorem, which extends the classical result of Benci-Rabinowitz [14, Theorem 5.29] to the above-mentioned setting, is then deduced.

How to cite

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Marano, Salvatore A., and Motreanu, Dumitru. "A critical point result for non-differentiable indefinite functionals." Commentationes Mathematicae Universitatis Carolinae 45.4 (2004): 663-679. <http://eudml.org/doc/249378>.

@article{Marano2004,
abstract = {In this paper, two deformation lemmas concerning a family of indefinite, non necessarily continuously differentiable functionals are proved. A critical point theorem, which extends the classical result of Benci-Rabinowitz [14, Theorem 5.29] to the above-mentioned setting, is then deduced.},
author = {Marano, Salvatore A., Motreanu, Dumitru},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {locally Lipschitz continuous and indefinite functionals; deformation lemmas; critical point theorems; critical points; Benci-Rabinowitz theorem; Palais-Smale condition; nonsmooth functionals},
language = {eng},
number = {4},
pages = {663-679},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A critical point result for non-differentiable indefinite functionals},
url = {http://eudml.org/doc/249378},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Marano, Salvatore A.
AU - Motreanu, Dumitru
TI - A critical point result for non-differentiable indefinite functionals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 4
SP - 663
EP - 679
AB - In this paper, two deformation lemmas concerning a family of indefinite, non necessarily continuously differentiable functionals are proved. A critical point theorem, which extends the classical result of Benci-Rabinowitz [14, Theorem 5.29] to the above-mentioned setting, is then deduced.
LA - eng
KW - locally Lipschitz continuous and indefinite functionals; deformation lemmas; critical point theorems; critical points; Benci-Rabinowitz theorem; Palais-Smale condition; nonsmooth functionals
UR - http://eudml.org/doc/249378
ER -

References

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  10. Du Y., A deformation lemma and some critical point theorems, Bull. Austral. Math. Soc. 43 (1991), 161-168. (1991) Zbl0714.58008MR1086730
  11. Ghoussoub N., Duality and Perturbation Methods in Critical Point Theory, Cambridge Tracts in Math. 107, Cambridge Univ. Press, Cambridge, 1993. Zbl1143.58300MR1251958
  12. Hofer H., On strongly indefinite functionals with applications, Trans. Amer. Math. Soc. 275 (1983), 185-214. (1983) Zbl0524.58010MR0678344
  13. Motreanu D., Varga C., Some critical point results for locally Lipschitz functionals, Comm. Appl. Nonlinear Anal. 4 (1997), 17-33. (1997) MR1460105
  14. Rabinowitz P.H., Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. in Math. 65, Amer. Math. Soc., Providence, 1986. Zbl0609.58002MR0845785
  15. Struwe M., Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Second Edition, Ergeb. Math. Grenzgeb. (3) 34, Springer Verlag, Berlin, 1996. MR1411681

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