On nontrivial solutions of a semilinear wave equation

Paul H. Rabinowitz

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1981)

  • Volume: 8, Issue: 4, page 647-657
  • ISSN: 0391-173X

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Rabinowitz, Paul H.. "On nontrivial solutions of a semilinear wave equation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 8.4 (1981): 647-657. <http://eudml.org/doc/83871>.

@article{Rabinowitz1981,
author = {Rabinowitz, Paul H.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {semilinear wave equation},
language = {eng},
number = {4},
pages = {647-657},
publisher = {Scuola normale superiore},
title = {On nontrivial solutions of a semilinear wave equation},
url = {http://eudml.org/doc/83871},
volume = {8},
year = {1981},
}

TY - JOUR
AU - Rabinowitz, Paul H.
TI - On nontrivial solutions of a semilinear wave equation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1981
PB - Scuola normale superiore
VL - 8
IS - 4
SP - 647
EP - 657
LA - eng
KW - semilinear wave equation
UR - http://eudml.org/doc/83871
ER -

References

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  1. [1] H. Amann, Saddle points and multiple solutions of differential equations, Math. Z., 169 (1979), pp. 127-166. Zbl0414.47042MR550724
  2. [2] H. Amann - E. Zehnder, Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa, 4, 7 (1980), pp. 539-603. Zbl0452.47077MR600524
  3. [3] A. Bahri - H. Brezis, Periodic solutions of a nonlinear wave equation, to appear Proc. Roy. Soc. Edinburgh. Zbl0438.35044MR574025
  4. [4] H. Brezis - J.M. Coron, Periodic solutions of nonlinear wave equations and Hamiltonian systems, preprint. Zbl0462.35004MR618324
  5. [5] H. Brezis - J.M. Coron - L. Nirenberg, Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz, preprint. Zbl0484.35057MR586417
  6. [6] H. Brezis - L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Scuola Norm. Sup. Pisa, 4, 5 (1978), pp. 225-326. Zbl0386.47035MR513090
  7. [7] H. Brezis - L. Nirenbfrg, Forced vibrations for a nonlinear wave equation, Comm. Pure Appl. Math., 31 (1978), pp. 1-30. Zbl0378.35040MR470377
  8. [8] J.M. Coron, Résolution de l'équation Au + Bu = f où A est linéaire autoadjoint et B déduit d'un potential convexe, to appear Ann. Fac. Sc. Toulouse. 
  9. [9] G. Mancini, Periodic solutions of some semi-linear autonomous wave equations, Boll. Un. Mat. Ital. (5), 15-B (1978), pp. 649-672. Zbl0393.35005MR518496
  10. [10] P.H. Rabinowitz, Some minimax theorems and applications to nonlinear partial differential equations, Nonlinear Analysis: A collection of papers in honor of Erich H. Rothe, Academic Press (1978), pp. 161-177. Zbl0466.58015MR501092
  11. [11] P.H. Rabinowitz, Free vibrations for a semilinear wave equation, Comm. Pure Appl. Math., 31 (1978), pp. 31-68. Zbl0341.35051MR470378
  12. [12] P.H. Rabinowitz, Subharmonic solutions of a forced wave equation, to appear Amer. J. Math. Zbl0563.35049MR648473
  13. [13] R.E.L. Turner, Superlinear Sturm-Liouville problems, J. Differential Equations, 13 (1973), pp. 157-171. Zbl0272.34031MR330610
  14. [14] P.H. Rabinowitz, Some aspects of nonlinear eigenvalue problems, Rocky Mountain J. Math., 3 (1973), pp. 161-202. Zbl0255.47069MR320850
  15. [15] R. Courant - D. Hilbert, Methods of Mathematical Physics, vol. I, Interscience (1953). Zbl0051.28802MR65391
  16. [16] E.A. Coddington - N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill (1955). Zbl0064.33002MR69338

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