Critical points of convex perturbations of some indefinite quadratic forms and semi-linear boundary value problems at resonance

J. Mawhin; M. Willem

Annales de l'I.H.P. Analyse non linéaire (1986)

  • Volume: 3, Issue: 6, page 431-453
  • ISSN: 0294-1449

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Mawhin, J., and 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 3.6 (1986): 431-453. <http://eudml.org/doc/78122>.

@article{Mawhin1986,
author = {Mawhin, J., Willem, M.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {dual least action principle; critical point; periodic solution; Hamiltonian systems; semilinear beam equations; averaging method},
language = {eng},
number = {6},
pages = {431-453},
publisher = {Gauthier-Villars},
title = {Critical points of convex perturbations of some indefinite quadratic forms and semi-linear boundary value problems at resonance},
url = {http://eudml.org/doc/78122},
volume = {3},
year = {1986},
}

TY - JOUR
AU - Mawhin, J.
AU - Willem, M.
TI - Critical points of convex perturbations of some indefinite quadratic forms and semi-linear boundary value problems at resonance
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1986
PB - Gauthier-Villars
VL - 3
IS - 6
SP - 431
EP - 453
LA - eng
KW - dual least action principle; critical point; periodic solution; Hamiltonian systems; semilinear beam equations; averaging method
UR - http://eudml.org/doc/78122
ER -

References

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  1. [1] S. Ahmad and A.C. Lazer, Critical point theory and a theorem of Amaral and Pera, Boll. Un. Mat. Ital., to appear. Zbl0603.34036
  2. [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. Zbl0351.35036MR427825
  3. [3] A. Bahri and H. Brezis, Periodic solutions of a nonlinear wave equation, Proc. Royal Soc. Edinburgh, t. A85, 1980, p. 313-320. Zbl0438.35044MR574025
  4. [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. Zbl0488.35008MR629433
  5. [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. Zbl0526.58016MR728984
  6. [6] M.S. Berger and M. Schechter, On the solvability of semilinear gradient operator equations, Adv. in Math., t. 25, 1977, p. 97-132. Zbl0354.47025MR500336
  7. [7] N.N. Bogoliubov and Yu.A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York, 1961. 
  8. [8] H. Brezis, Periodic solutions of nonlinear vibrating strings and duality principles, Bull. Amer. Math. Soc., (NS), t. 8, 1983, p. 409-426. Zbl0515.35060MR693957
  9. [9] F. Clarke and I. Ekeland, Hamiltonian trajectories with prescribed minimal period, Comm. Pure Appl. Math., t. 33, 1980, p. 103-116. Zbl0403.70016MR562546
  10. [10] J.L. Kazdan and F. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math., t. 28, 1975, p. 567-597. Zbl0325.35038MR477445
  11. [11] K. Klingelhofer, Nonlinear boundary value problems with simple eigenvalue of the linear part, Arch. Rat. Mech. Analysis, t. 37, 1970, p. 381-398. Zbl0212.13201MR259684
  12. [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. Zbl0547.34032MR753881
  13. [13] J. Mawhin, A Neumann boundary value problem with jumping monotone nonlinearity, Delft Progress Report, t. 10, 1985, p. 44-52. Zbl0595.35050MR787670
  14. [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. [15] J. Mawhin, Points fixes, points critiques et problèmes aux limites, Sém. Math. Supé- rieures, Press. Univ. Montreal, 1985. Zbl0561.34001MR789982
  16. [16] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, in preparation. 
  17. [17] J. Mawhin, J.R. Ward and M. Willem, Variational methods and semilinear elliptic equations, Arch. Rat. Mech. Anal., in press. Zbl0656.35044
  18. [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. Zbl0559.34014MR776200
  19. [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. Zbl0466.58015MR501092

Citations in EuDML Documents

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  1. Xianhua Tang, Xingyong Zhang, Periodic solutions for second-order Hamiltonian systems with a p -Laplacian
  2. Xingyong Zhang, Xianhua Tang, Periodic solutions for second-order Hamiltonian systems with a p-Laplacian
  3. Qiongfen Zhang, X. H. Tang, Periodic solutions for second order Hamiltonian systems
  4. Peng Chen, Xianhua Tang, Existence of solutions for a class of second-order p -Laplacian systems with impulsive effects
  5. Martin Schechter, A generalization of the saddle point method with applications

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