Multiple Critical Points of Perturbed Symmetric Strongly Indefinite Functionals
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 2, p. 675-688
@article{AIHPC_2009__26_2_675_0,
author = {Bonheure, Denis and Ramos, Miguel},
title = {Multiple Critical Points of Perturbed Symmetric Strongly Indefinite Functionals},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {26},
number = {2},
year = {2009},
pages = {675-688},
doi = {10.1016/j.anihpc.2008.06.002},
zbl = {1163.35013},
mrnumber = {2504048},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2009__26_2_675_0}
}

Bonheure, Denis; Ramos, Miguel. Multiple Critical Points of Perturbed Symmetric Strongly Indefinite Functionals. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 2, pp. 675-688. doi : 10.1016/j.anihpc.2008.06.002. http://www.numdam.org/item/AIHPC_2009__26_2_675_0/

[1] Angenent S., Van Der Vorst R., A Superquadratic Indefinite Elliptic System and Its Morse-Conley-Floer Homology, Math. Z. 231 (1999) 203-248. | MR 1703347 | Zbl 0939.58015

[2] Bahri A., Topological Results on a Certain Class of Functionals and Application, J. Funct. Anal. 41 (1981) 397-427. | MR 619960 | Zbl 0499.35050

[3] Bahri A., Berestycki H., A Perturbation Method in Critical Point Theory and Applications, Trans. Amer. Math. Soc. 267 (1981) 1-32. | MR 621969 | Zbl 0476.35030

[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. | MR 968487 | Zbl 0645.58013

[5] Bolle Ph., Ghoussoub N., Tehrani H., The Multiplicity of Solutions to Non-Homogeneous Boundary Value Problems, Manuscripta Math. 101 (2000) 325-350. | MR 1751037 | Zbl 0963.35001

[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. | MR 2170556 | Zbl 1137.35357

[7] Clapp M., Ding Y., Hernández-Linares S., Strongly Indefinite Functionals With Perturbed Symmetries and Multiple Solutions of Nonsymmetric Elliptic Systems, Electronic J. Differential Equations 2004 (100) (2004) 1-18. | MR 2108871 | Zbl 1109.35324

[8] Clement P., De Figueiredo D. G., Mitidieri E., Positive Solutions of Semilinear Elliptic Systems, Comm. Partial Differential Equations 17 (1992) 923-940. | MR 1177298 | Zbl 0818.35027

[9] Cwickel M., Weak Type Estimates and the Number of Bound States of Schrödinger Operators, Ann. Math. 106 (1977) 93-102. | Zbl 0362.47006

[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. | MR 1975408 | Zbl 1125.35338

[11] De Figueiredo D. G., Felmer P., On Superquadratic Elliptic Systems, Trans. Amer. Math. Soc. 343 (1994) 97-116. | MR 1214781 | Zbl 0799.35063

[12] Hulshof J., Van Der Vorst R., Differential Systems With Strongly Indefinite Variational Structure, J. Funct. Anal. 114 (1993) 32-58. | MR 1220982 | Zbl 0793.35038

[13] Kajikiya R., Radially Symmetric Solutions of Semilinear Elliptic Equations, Existence and Sobolev Estimates, Hiroshima Math. J. 21 (1991) 111-161. | MR 1091434 | Zbl 0736.35046

[14] Kajikiya R., Tanaka K., Existence of Infinitely Many Solutions for Some Superlinear Elliptic Equations, J. Math. Anal. Appl. 149 (1990) 313-321. | MR 1057676 | Zbl 0716.35028

[15] Lieb E. H., Bounds on the Eigenvalues of the Laplace and Schrödinger Operators, Bull. Amer. Math. Soc. 82 (1976) 751-753. | MR 407909 | Zbl 0329.35018

[16] Rabinowitz P., Multiple Critical Points of Perturbed Symmetric Functionals, Trans. Amer. Math. Soc. 272 (1982) 753-770. | MR 662065 | Zbl 0589.35004

[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. | MR 845785 | Zbl 0609.58002

[18] Ramos M., Tavares H., Solutions With Multiple Spike Patterns for an Elliptic System, Calc. Var. Partial Differential Equations 31 (2008) 1-25. | MR 2342612 | Zbl 1143.35027

[19] Ramos M., Yang J., Spike-Layered Solutions for an Elliptic System With Neumann Boundary Conditions, Trans. Amer. Math. Soc. 357 (2005) 3265-3284. | MR 2135746 | Zbl 1136.35046

[20] Rosenbljum G., The Distribution of the Discrete Spectrum for Singular Differential Operators, Soviet Math. Dokl. 13 (1972) 245-249. | Zbl 0249.35069

[21] Schechter M., Zou W., Infinitely Many Solutions to Perturbed Elliptic Equations, J. Funct. Anal. 228 (2005) 1-38. | MR 2170983 | Zbl 1139.35346

[22] Simon B., Functional Integration and Quantum Physics, Academic Press, 1979. | MR 544188 | Zbl 0434.28013

[23] Sirakov B., On the Existence of Solutions of Hamiltonian Elliptic Systems in ${R}^{N}$, Adv. Differential Equations 5 (2000) 1445-1464. | MR 1785681 | Zbl pre01700732

[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. | MR 595426 | Zbl 0456.35031

[25] Struwe M., Superlinear Elliptic Boundary Value Problems With Rotational Symmetry, Arch. Math. (Basel) 39 (1982) 233-240. | MR 682450 | Zbl 0496.35034

[26] Tanaka K., Morse Indices at Critical Points Related to the Symmetric Mountain Pass Theorem and Applications, Comm. Partial Differential Equations 14 (1989) 99-128. | MR 973271 | Zbl 0669.34035

[27] Tarsi C., Perturbation From Symmetry and Multiplicity of Solutions for Strongly Indefinite Elliptic Systems, Adv. Nonlinear Stud. 7 (2007) 1-30. | MR 2287525 | Zbl pre05182588

[28] Tehrani H. T., Infinitely Many Solutions for Indefinite Semilinear Elliptic Equations Without Symmetry, Comm. Partial Differential Equations 21 (1996) 541-557. | MR 1387459 | Zbl 0855.35044