| Title:
|
A critical point result for non-differentiable indefinite functionals (English) |
| Author:
|
Marano, Salvatore A. |
| Author:
|
Motreanu, Dumitru |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
663-679 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
locally Lipschitz continuous and indefinite functionals |
| Keyword:
|
deformation lemmas |
| Keyword:
|
critical point theorems |
| MSC:
|
35A15 |
| MSC:
|
47J30 |
| MSC:
|
49J35 |
| MSC:
|
49J52 |
| MSC:
|
58E05 |
| idZBL:
|
Zbl 1107.49005 |
| idMR:
|
MR2103082 |
| . |
| Date available:
|
2009-05-05T16:48:15Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119492 |
| . |
| Reference:
|
[1] Barletta G.: Applications of a critical point result for non-differentiable indefinite functionals.preprint. |
| Reference:
|
[2] Barletta G., Marano S.A.: Some remarks on critical point theory for locally Lipschitz functions.Glasgow Math. J. 45 (2003), 131-141. Zbl 1101.58009, MR 1972703 |
| Reference:
|
[3] Bartolo P., Benci V., Fortunato D.: Abstract critical point theorems and applications to some nonlinear problems with ``strong'' resonance at infinity.Nonlinear Anal. 7 (1983), 981-1012. Zbl 0522.58012, MR 0713209 |
| Reference:
|
[4] Benci V., Rabinowitz P.H.: Critical point theorems for indefinite functionals.Invent. Math. 52 (1979), 241-273. Zbl 0465.49006, MR 0537061 |
| Reference:
|
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| Reference:
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| Reference:
|
[7] Clarke F.H.: Optimization and Nonsmooth Analysis.Classics in Applied Mathematics 5, SIAM, Philadelphia, 1990. Zbl 0696.49002, MR 1058436 |
| Reference:
|
[8] Costa D.G., Magalh aes C.: A unified approach to a class of strongly indefinite functionals.J. Differential Equations 125 (1996), 521-547. MR 1378765 |
| Reference:
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[9] Ding Y.: A remark on the linking theorem with applications.Nonlinear Anal. 22 (1994), 237-250. Zbl 0798.58014, MR 1258960 |
| Reference:
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[10] Du Y.: A deformation lemma and some critical point theorems.Bull. Austral. Math. Soc. 43 (1991), 161-168. Zbl 0714.58008, MR 1086730 |
| Reference:
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[11] Ghoussoub N.: Duality and Perturbation Methods in Critical Point Theory.Cambridge Tracts in Math. 107, Cambridge Univ. Press, Cambridge, 1993. Zbl 1143.58300, MR 1251958 |
| Reference:
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[12] Hofer H.: On strongly indefinite functionals with applications.Trans. Amer. Math. Soc. 275 (1983), 185-214. Zbl 0524.58010, MR 0678344 |
| Reference:
|
[13] Motreanu D., Varga C.: Some critical point results for locally Lipschitz functionals.Comm. Appl. Nonlinear Anal. 4 (1997), 17-33. MR 1460105 |
| Reference:
|
[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. Zbl 0609.58002, MR 0845785 |
| Reference:
|
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| . |
