Multiple critical points of perturbed symmetric strongly indefinite functionals
Annales de l'I.H.P. Analyse non linéaire (2009)
- Volume: 26, Issue: 2, page 675-688
- ISSN: 0294-1449
Access Full Article
topHow to cite
topBonheure, Denis, and Ramos, Miguel. "Multiple critical points of perturbed symmetric strongly indefinite functionals." Annales de l'I.H.P. Analyse non linéaire 26.2 (2009): 675-688. <http://eudml.org/doc/78860>.
@article{Bonheure2009,
author = {Bonheure, Denis, Ramos, Miguel},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {elliptic system; strongly indefinite functional; perturbation from symmetry; Lyapunov-Schmidt reduction; genericity},
language = {eng},
number = {2},
pages = {675-688},
publisher = {Elsevier},
title = {Multiple critical points of perturbed symmetric strongly indefinite functionals},
url = {http://eudml.org/doc/78860},
volume = {26},
year = {2009},
}
TY - JOUR
AU - Bonheure, Denis
AU - Ramos, Miguel
TI - Multiple critical points of perturbed symmetric strongly indefinite functionals
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 2
SP - 675
EP - 688
LA - eng
KW - elliptic system; strongly indefinite functional; perturbation from symmetry; Lyapunov-Schmidt reduction; genericity
UR - http://eudml.org/doc/78860
ER -
References
top- [1] Angenent S., van der Vorst R., A superquadratic indefinite elliptic system and its Morse–Conley–Floer homology, Math. Z.231 (1999) 203-248. Zbl0939.58015MR1703347
- [2] Bahri A., Topological results on a certain class of functionals and application, J. Funct. Anal.41 (1981) 397-427. Zbl0499.35050MR619960
- [3] Bahri A., Berestycki H., A perturbation method in critical point theory and applications, Trans. Amer. Math. Soc.267 (1981) 1-32. Zbl0476.35030MR621969
- [4] Bahri A., Lions P.L., Morse-index of some min-max critical points. I. Application to multiplicity results, Comm. Pure Appl. Math.41 (1988) 1027-1037. Zbl0645.58013MR968487
- [5] Bolle Ph., Ghoussoub N., Tehrani H., The multiplicity of solutions to non-homogeneous boundary value problems, Manuscripta Math.101 (2000) 325-350. Zbl0963.35001MR1751037
- [6] Castro A., Clapp M., Upper estimates for the energy of solutions of nonhomogeneous boundary value problems, Proc. Amer. Math. Soc.134 (2006) 167-175. Zbl1137.35357MR2170556
- [7] Clapp M., Ding Y., Hernández-Linares S., Strongly indefinite functionals with perturbed symmetries and multiple solutions of nonsymmetric elliptic systems, Electronic J. Differential Equations2004 (100) (2004) 1-18. Zbl1109.35324MR2108871
- [8] Clement P., de Figueiredo D.G., Mitidieri E., Positive solutions of semilinear elliptic systems, Comm. Partial Differential Equations17 (1992) 923-940. Zbl0818.35027MR1177298
- [9] Cwickel M., Weak type estimates and the number of bound states of Schrödinger operators, Ann. Math.106 (1977) 93-102. Zbl0362.47006
- [10] de Figueiredo D.G., Ding Y.H., Strongly indefinite functionals and multiple solutions of elliptic systems, Trans. Amer. Math. Soc.355 (2003) 2973-2989. Zbl1125.35338MR1975408
- [11] de Figueiredo D.G., Felmer P., On superquadratic elliptic systems, Trans. Amer. Math. Soc.343 (1994) 97-116. Zbl0799.35063MR1214781
- [12] Hulshof J., van der Vorst R., Differential systems with strongly indefinite variational structure, J. Funct. Anal.114 (1993) 32-58. Zbl0793.35038MR1220982
- [13] Kajikiya R., Radially symmetric solutions of semilinear elliptic equations, existence and Sobolev estimates, Hiroshima Math. J.21 (1991) 111-161. Zbl0736.35046MR1091434
- [14] Kajikiya R., Tanaka K., Existence of infinitely many solutions for some superlinear elliptic equations, J. Math. Anal. Appl.149 (1990) 313-321. Zbl0716.35028MR1057676
- [15] Lieb E.H., Bounds on the eigenvalues of the Laplace and Schrödinger operators, Bull. Amer. Math. Soc.82 (1976) 751-753. Zbl0329.35018MR407909
- [16] Rabinowitz P., Multiple critical points of perturbed symmetric functionals, Trans. Amer. Math. Soc.272 (1982) 753-770. Zbl0589.35004MR662065
- [17] Rabinowitz P., Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. in Math., vol. 65, Amer. Math. Soc., Providence, RI, 1986. Zbl0609.58002MR845785
- [18] Ramos M., Tavares H., Solutions with multiple spike patterns for an elliptic system, Calc. Var. Partial Differential Equations31 (2008) 1-25. Zbl1143.35027MR2342612
- [19] Ramos M., Yang J., Spike-layered solutions for an elliptic system with Neumann boundary conditions, Trans. Amer. Math. Soc.357 (2005) 3265-3284. Zbl1136.35046MR2135746
- [20] Rosenbljum G., The distribution of the discrete spectrum for singular differential operators, Soviet Math. Dokl.13 (1972) 245-249. Zbl0249.35069
- [21] Schechter M., Zou W., Infinitely many solutions to perturbed elliptic equations, J. Funct. Anal.228 (2005) 1-38. Zbl1139.35346MR2170983
- [22] Simon B., Functional Integration and Quantum Physics, Academic Press, 1979. Zbl0434.28013MR544188
- [23] Sirakov B., On the existence of solutions of Hamiltonian elliptic systems in , Adv. Differential Equations5 (2000) 1445-1464. Zbl1213.35223MR1785681
- [24] Struwe M., Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems, Manuscripta Math.32 (1980) 335-364. Zbl0456.35031MR595426
- [25] Struwe M., Superlinear elliptic boundary value problems with rotational symmetry, Arch. Math. (Basel)39 (1982) 233-240. Zbl0496.35034MR682450
- [26] Tanaka K., Morse indices at critical points related to the symmetric mountain pass theorem and applications, Comm. Partial Differential Equations14 (1989) 99-128. Zbl0669.34035MR973271
- [27] Tarsi C., Perturbation from symmetry and multiplicity of solutions for strongly indefinite elliptic systems, Adv. Nonlinear Stud.7 (2007) 1-30. Zbl05182588MR2287525
- [28] Tehrani H.T., Infinitely many solutions for indefinite semilinear elliptic equations without symmetry, Comm. Partial Differential Equations21 (1996) 541-557. Zbl0855.35044MR1387459
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.