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Periodic solutions of a nonlinear wave equation

  • Abbas Bahri (a1) and Haïm Brezis (a1)
Synopsis
Synopsis

We provide a sufficient and “almost” necessary condition for the existence of a periodic solution of the equation

where F is nondecreasing in u and has a small linear growth as |u|→∞.

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References
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1Brezis H. and Nirenberg L.. Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Ann. Scuola Norm. Sup. Pisa 5 (1978), 225326.
2Brezis H. and Nirenberg L.. Forced vibrations for a nonlinear wave equation. Comm. Pure Appl. Math. 31 (1978), 130.
3De Simon L. and Torelli G.. Soluzione periodiche di equazioni parziali di tipo iperbolico nonlineari. Rend. Sem. Mat. Univ. Padova 40 (1968), 380401.
4Landesman E. and Lazer A.. Nonlinear perturbations of linear elliptic boundary value problems at resonance. J. Math. Mech. 19 (1970), 609623.
5Lovicarova H.. Periodic solutions of a weakly nonlinear wave equation in one dimension. Czechoslovak Math. J. 19 (1969), 324342.
6Mancini G.. Periodic solutions of semilinear autonomous wave equation, to appear.
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8Rabinowitz P.. Periodic solutions of nonlinear hyperbolic partial differential equations. Comm. Pure Appl. Math. 20 (1967), 145205.
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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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