Critical points of convex perturbations of some indefinite quadratic forms and semi-linear boundary value problems at resonance
Annales de l'I.H.P. Analyse non linéaire, Volume 3 (1986) no. 6, p. 431-453
@article{AIHPC_1986__3_6_431_0,
author = {Mawhin, Jean and Willem, M.},
title = {Critical points of convex perturbations of some indefinite quadratic forms and semi-linear boundary value problems at resonance},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Gauthier-Villars},
volume = {3},
number = {6},
year = {1986},
pages = {431-453},
zbl = {0678.35091},
mrnumber = {870864},
language = {en},
url = {http://www.numdam.org/item/AIHPC_1986__3_6_431_0}
}

Mawhin, J.; Willem, M. Critical points of convex perturbations of some indefinite quadratic forms and semi-linear boundary value problems at resonance. Annales de l'I.H.P. Analyse non linéaire, Volume 3 (1986) no. 6, pp. 431-453. http://www.numdam.org/item/AIHPC_1986__3_6_431_0/

[1] S. Ahmad and A.C. Lazer, Critical point theory and a theorem of Amaral and Pera, Boll. Un. Mat. Ital., to appear. | Zbl 0603.34036

[2] S. Ahmad, A.C. Lazer and J.L. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J., t. 25, 1976, p. 933-944. | MR 427825 | Zbl 0351.35036

[3] A. Bahri and H. Brezis, Periodic solutions of a nonlinear wave equation, Proc. Royal Soc. Edinburgh, t. A85, 1980, p. 313-320. | MR 574025 | Zbl 0438.35044

[4] A. Bahri and L. Sanchez, Periodic solutions of a nonlinear telegraph equation in one dimension, Boll. Un. Nat. Ital., t. 5, 18-B, 1981, p. 709-720. | MR 629433 | Zbl 0488.35008

[5] H. Berestycki, Solutions périodiques des systèmes hamiltoniens, in Séminaire Bourbaki, 1982-1983, Astérique, p. 105-106, Soc. Math. France, Paris, 1983, p. 105-128. | Numdam | MR 728984 | Zbl 0526.58016

[6] M.S. Berger and M. Schechter, On the solvability of semilinear gradient operator equations, Adv. in Math., t. 25, 1977, p. 97-132. | MR 500336 | Zbl 0354.47025

[7] N.N. Bogoliubov and Yu.A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York, 1961.

[8] H. Brezis, Periodic solutions of nonlinear vibrating strings and duality principles, Bull. Amer. Math. Soc., (NS), t. 8, 1983, p. 409-426. | MR 693957 | Zbl 0515.35060

[9] F. Clarke and I. Ekeland, Hamiltonian trajectories with prescribed minimal period, Comm. Pure Appl. Math., t. 33, 1980, p. 103-116. | MR 562546 | Zbl 0403.70016

[10] J.L. Kazdan and F. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math., t. 28, 1975, p. 567-597. | MR 477445 | Zbl 0325.35038

[11] K. Klingelhofer, Nonlinear boundary value problems with simple eigenvalue of the linear part, Arch. Rat. Mech. Analysis, t. 37, 1970, p. 381-398. | MR 259684 | Zbl 0212.13201

[12] J. Mawhin, Remarks on the preceding paper of Ahmad and Lazer on periodic solutions, Boll. Un. Mat. Ital., t. 6, 3-A, 1984, p. 229-238. | MR 753881 | Zbl 0547.34032

[13] J. Mawhin, A Neumann boundary value problem with jumping monotone nonlinearity, Delft Progress Report, t. 10, 1985, p. 44-52. | MR 787670 | Zbl 0595.35050

[14] J. Mawhin, The dual least action principle and nonlinear differential equations, in Intern. Conf. Qualitative Theory of Differential Equations, Edmonton, 1984, to appear.

[15] J. Mawhin, Points fixes, points critiques et problèmes aux limites, Sém. Math. Supé- rieures, Press. Univ. Montreal, 1985. | MR 789982 | Zbl 0561.34001

[16] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, in preparation.

[17] J. Mawhin, J.R. Ward and M. Willem, Variational methods and semilinear elliptic equations, Arch. Rat. Mech. Anal., in press. | Zbl 0656.35044

[18] J. Mawhin, J.R. Ward and M. Willem, Necessary and sufficient conditions for the solvability of a nonlinear two-point boundary value problem, Proc. Amer. Math. Soc., t. 93, 1985, p. 667-674. | MR 776200 | Zbl 0559.34014

[19] P. Rabinowitz, Some minimax theorems and applications to nonlinear partial differential equations, in Nonlinear Analysis, Cesari, Kannan and Weinberger ed., Academic Press, 1978, p. 161-177. | MR 501092 | Zbl 0466.58015