| Title:
|
A nonlinear periodic system with nonsmooth potential of indefinite sign (English) |
| Author:
|
Filippakis, Michael E. |
| Author:
|
Papageorgiou, Nikolaos S. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
205-213 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider a nonlinear periodic system driven by the vector ordinary $p$-Laplacian and having a nonsmooth locally Lipschitz potential, which is positively homogeneous. Using a variational approach which exploits the homogeneity of the potential, we establish the existence of a nonconstant solution. (English) |
| Keyword:
|
locally Lipschitz function |
| Keyword:
|
generalized subdifferential |
| Keyword:
|
$p$-Laplacian |
| Keyword:
|
homogeneous function |
| Keyword:
|
variational method |
| Keyword:
|
Poincare-Wirtinger inequality |
| Keyword:
|
potential indefinite in sign |
| MSC:
|
34A60 |
| MSC:
|
34B15 |
| MSC:
|
34C25 |
| MSC:
|
47J30 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1164.34404 |
| idMR:
|
MR2260378 |
| . |
| Date available:
|
2008-06-06T22:48:02Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107998 |
| . |
| Reference:
|
[1] Adly S., Goeleven D.: Homoclinic orbits for a class of hemivariational inequalities.Appl. Anal. 58 (1995), 229–240. Zbl 0829.49007, MR 1383190 |
| Reference:
|
[2] Adly S., Goeleven D., Motreanu D.: Periodic and homoclinic solutions for a class of unilateral problems.Discrete Contin. Dynam. Systems 3 (1997), 579–590. Zbl 0948.37013, MR 1465127 |
| Reference:
|
[3] Adly S., Motreanu D.: Periodic solutions for second-order differential equations involving nonconvex superpotentials.J. Global Optim. 17 (2000), 9–17. Zbl 1055.34080, MR 1807964 |
| Reference:
|
[4] Antonacci F.: Existence of periodic solutions of Hamiltonian systems with potential indefinite in sign.Nonlinear Anal. 29 (1997), 1353–1364. Zbl 0894.34036, MR 1484908 |
| Reference:
|
[5] Ben Naoum A. K., Troestler C., Willem M.: Existence and multiplicity results for homogeneous second order differential equations.J. Differential Equations 112 (1994), 239–249. Zbl 0808.58013, MR 1287560 |
| Reference:
|
[6] Clarke F. H.: A new approach to Lagrange multipliers.Math. Oper. Res. I (1976), 165–174. Zbl 0404.90100, MR 0414104 |
| Reference:
|
[7] Denkowski Z., Migorski S., Papageorgiou N. S.: An introduction to Nonlinear Analysis. Theory.Kluwer/Plenum, New York (2003). Zbl 1040.46001, MR 2024162 |
| Reference:
|
[8] Denkowski Z., Migorski S., Papageorgiou N. S.: An introduction to Nonlinear Analysis. Applications.Kluwer/Plenum, New York (2003). Zbl 1054.47001, MR 2024161 |
| Reference:
|
[9] Girardi M., Matzeu M.: Existence and multiplicity results for periodic solutions for superquadratic systems where the potential changes sign.Nonlinear Differential Equations Appl. 2 (1995), 35–61. MR 1322202 |
| Reference:
|
[10] Lassoued L.: Solutions periodiques d’un systeme differentiel non lineaire du second order avec changement de sign.Ann. Math. Pura Appl. 156 (1990), 76–111. MR 1080211 |
| Reference:
|
[11] Lassoued L.: Periodic solutions of a second order superquadratic system with a change of sign in the potential.J. Differential Equations 93 (1991), 1–18. Zbl 0736.34041, MR 1122304 |
| Reference:
|
[12] Papageorgiou E. H., Papageorgiou N. S.: Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems.Czechoslovak Math. J. 54 (2004), 347–371. Zbl 1080.34532, MR 2059256 |
| Reference:
|
[13] Tang C. L., Wu X. P.: Periodic solutions for second order Hamiltonian systems with a change sign potential.J. Math. Anal. 292 (2004), 506–516. Zbl 1078.34023, MR 2047627 |
| Reference:
|
[14] Xu Y. T., Guo Z. M.: Existence of periodic solutions to second-order Hamiltonian systems with potential indefinite in sign.Nonlinear Anal. 51 (2002), 1273–1283. Zbl 1157.37329, MR 1926629 |
| . |
