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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A wave equation with a possibly jumping nonlinearity
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by J. R. Ward PDF
Proc. Amer. Math. Soc. 92 (1984), 209-214 Request permission

Abstract:

Existence of a doubly periodic solution to a forced semilinear wave equation is established. The nonlinearity may "jump" across any finite number of eigenvalues of finite multiplicity.
References
  • Shui Nee Chow and Jack K. Hale, Methods of bifurcation theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 251, Springer-Verlag, New York-Berlin, 1982. MR 660633
  • Hana Lovicarová, Periodic solutions of a weakly nonlinear wave equation in one dimension, Czechoslovak Math. J. 19(94) (1969), 324–342. MR 247249
  • Jean Mawhin, Periodic solutions of nonlinear dispersive wave equations, Constructive methods for nonlinear boundary value problems and nonlinear oscillations (Proc. Conf., Math. Res. Inst., Oberwolfach, 1978), Internat. Ser. Numer. Math., vol. 48, Birkhäuser, Basel-Boston, Mass., 1979, pp. 102–109. MR 565644
    • —, Compacité, monotonie et convexité dans l’etude de problèmes aux limites semi-linéaires, Séminaire d’Analyse Moderne, No. 19, Univ. de Sherbrooke, 1981. J. Mawhin and J. Ward, Asymptotic nonuniform non-resonance conditions in the periodic Dirichlet problem for semi-linear wave equations, J. Math. Pures Appl. (to appear). —, Nonuniform non-resonance conditions in the periodic-Dirichlet problem for semi-linear wave equations with jumping nonlinearities (to appear).
  • Michel Willem, Periodic solutions of wave equations with jumping nonlinearities, J. Differential Equations 36 (1980), no. 1, 20–27. MR 571124, DOI 10.1016/0022-0396(80)90072-8
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 209-214
  • MSC: Primary 35B10; Secondary 35L70
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0754705-4
  • MathSciNet review: 754705