Existence of solutions of nonlinear hyperbolic equations

L. Cesari; R. Kannan

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1979)

  • Volume: 6, Issue: 4, page 573-592
  • ISSN: 0391-173X

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Cesari, L., and Kannan, R.. "Existence of solutions of nonlinear hyperbolic equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.4 (1979): 573-592. <http://eudml.org/doc/83821>.

@article{Cesari1979,
author = {Cesari, L., Kannan, R.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {existence of solutions; operational equation in real Hilbert spaces; problem at resonance; hyperbolic problems},
language = {eng},
number = {4},
pages = {573-592},
publisher = {Scuola normale superiore},
title = {Existence of solutions of nonlinear hyperbolic equations},
url = {http://eudml.org/doc/83821},
volume = {6},
year = {1979},
}

TY - JOUR
AU - Cesari, L.
AU - Kannan, R.
TI - Existence of solutions of nonlinear hyperbolic equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1979
PB - Scuola normale superiore
VL - 6
IS - 4
SP - 573
EP - 592
LA - eng
KW - existence of solutions; operational equation in real Hilbert spaces; problem at resonance; hyperbolic problems
UR - http://eudml.org/doc/83821
ER -

References

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  1. [1] J.P. Aubin, Un théorème de compacité, C. R. Acad. Sci. Paris, 256 (1963), pp. 5042-5044. Zbl0195.13002MR152860
  2. [2] G. Bachman - L. Narici, Functional Analysis, Academic Press, 1966. Zbl0141.11502MR217549
  3. [3] L. Cesari, Functional analysis, nonlinear differential equations, and the alternative method, in Functional Analysis and Nonlinear Differential Equations (L. Cesari, R. Kannan, J. D. Schuur, eds.), Dekker, New York, 1976, pp. 1-197. Zbl0343.47038MR487630
  4. [4] L. Cesari, An abstract existence theorem across a point of resonance, in Dynamical Systems, an International Symposium (A. R. Bednarek and L. Cesari, eds.), Academic Press (1977), pp. 11-26. Zbl0554.34001MR467420
  5. [5] L. Cesari, Nonlinear oscillations across a point of resonance for nonselfadjoint systems, J. Differential Equations, 28 (1978), pp. 43-59. Zbl0395.34034MR477909
  6. [6] L. Cesari, Nonlinear problems across a point of resonance for nonselfadjoint systems, in Nonlinear Analysis (a volume in honor of E. H. Rothe (L. Cesari, R. Kannan and F. Weinberger, eds.), Academic Press (1978), pp. 43-67. Zbl0463.47044MR499091
  7. [7] L. Cesari - R. Kannan, Functional analysis and nonlinear differential equations, Bull. Amer. Math. Soc., 79 (1973), pp. 1216-1219. Zbl0278.47039MR333861
  8. [8] L. Cesari - R. Kannan, An abstract existence theorem at resonance, Proc. Amer. Math. Soc., 63 (1977), pp. 221-225. Zbl0361.47021MR448180
  9. [9] L. Cesari - R. Kannan, Solutions of nonlinear hyperbolic equations at resonanceNonlinear Analysis., to appear. Zbl0495.35007MR671720
  10. [10] L. Cesari - P.J. Mckenna, Alternative problems and Grothendieck approximation properties. Bulletin Inst. Math. Sinica, Taiwan, 6 (1978), pp. 569-581. Zbl0411.46010MR528669
  11. [11] W.S. Hall, On the existence of periodic solutions for the equation Dttu + + (- 1)pD2pxu = εf(·,·, u), J. Differential Equations, 7 (1970), pp. 509-526. Zbl0198.14002
  12. [12] W.S. Hall, Periodic solutions of a class of weakly nonlinear evolution equations, Arch. Rational Mech. Anal., 39 (1970), pp. 294-322. Zbl0211.12704MR274914
  13. [13] R. Kannan - P.J. Mckenna, An existence theorem by alternative method for semilinear abstract equations, Boll. Un. Mat. Ital., (5),14-A (1977), pp. 355-358. Zbl0352.47030MR500347
  14. [14] P.J. Mckenna, Nonselfadjoint semilinear equations at multiple resonance in the alternative method, J. Differential Equations, 33 (1979), no. 3. Zbl0436.34055MR543700
  15. [15] H. Petzeltova, Periodic solutions of the equation utt + uxxxx = f(·, ·, u, ut), Czechoslovak Math. J., 23 (98) (1973), pp. 269-285. Zbl0263.35017MR328286
  16. [16] E.H. Rothe, On the Cesari index and the Browder-Petryshyn degree, in Dynamical Systems, An International Symposium (A. R. Bednarek and L. Cesari, eds.), Academic Press (1977), pp. 295-312. Zbl0571.47052MR455032

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