Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Doubly-periodic solutions of a forced semilinear wave equation


Authors: M. Arias, P. Martínez-Amores and R. Ortega
Journal: Proc. Amer. Math. Soc. 101 (1987), 503-508
MSC: Primary 35L70; Secondary 35B10
DOI: https://doi.org/10.1090/S0002-9939-1987-0908657-7
MathSciNet review: 908657
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Existence results are obtained for doubly-periodic solutions of a semilinear wave equation when the nonlinearity is bounded in one side.


References [Enhancements On Off] (What's this?)

  • [1] A. Bahri and H. Brezis, Periodic solution of a nonlinear wave equations, Proc. Roy. Soc. Edinburgh Sect. A 85 (1980), 313-320. MR 574025 (82f:35011)
  • [2] H. Brezis, Periodic solutions of nonlinear vibrating strings and duality principles, Bull. Amer. Math. Soc. (N.S) 8 (1983), 409-426. MR 693957 (84e:35010)
  • [3] H. Brezis and L. Nirenberg, Forced vibrations for a nonlinear wave equation, Comm. Pure Appl. Math. 31 (1978), 1-30. MR 470377 (81i:35112)
  • [4] S.-N. Chow and J. Hale, Methods of bifurcation theory, Springer-Verlag, Berlin and New York, 1982. MR 660633 (84e:58019)
  • [5] R. Kannan and R. Ortega, Periodic solution of pendulum-type equations, J. Differential Equation 59 (1985), 123-144. MR 803090 (87f:34045)
  • [6] N. Krylová and O. Vejvoda, A linear and weakly nonlinear equation of a beam: The boundary-value problem for free extremities and its periodic solution, Czechoslovak Math. J. 21 (96) (1971), 535-566. MR 0289918 (44:7103)
  • [7] J. Ward, Asumptotic conditions for periodic solutions of ordinary differential equations, Proc. Amer. Math. Soc. 81 (1981), 415-420. MR 597653 (82a:34057)
  • [8] -, A wave equation with a possibly jumping nonlinearity, Proc. Amer. Math. Soc. 92 (1984), 209-214. MR 754705 (86a:35012)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35L70, 35B10

Retrieve articles in all journals with MSC: 35L70, 35B10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0908657-7
Keywords: Nonlinear wave equation, doubly periodic solutions, resonance, $ {L^\infty }$-bounds
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society