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Periodic solutions of a nonlinear wave equation

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

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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3De Simon L. and Torelli G.. Soluzione periodiche di equazioni parziali di tipo iperbolico nonlineari. Rend. Sem. Mat. Univ. Padova 40 (1968), 380401.
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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.
7Mawhin J.. Periodic solutions of nonlinear dispersive wave equation, to appear.
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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