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)

 
 

 

Resonance and non-resonance
in a problem of boundedness


Authors: Rafael Ortega and Antonio Tineo
Journal: Proc. Amer. Math. Soc. 124 (1996), 2089-2096
MSC (1991): Primary 34B15, 34C11
DOI: https://doi.org/10.1090/S0002-9939-96-03457-0
MathSciNet review: 1342038
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper studies the existence of bounded solutions of a forced non-linear differential equation of arbitrary order. Necessary and sufficient conditions for the existence of such solutions are obtained. These results are inspired by classical results on the periodic problem, both in the resonant and non-resonant cases.


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

  • 1. S. Ahmad, A nonstandard resonance problem for ordinary differential equations, Trans. Am. Math. Soc, 323 (1991), 857-875. MR 91e:34046
  • 2. W. A. Coppel, Dichotomies in Stability Theory, Lectures Notes in Math 629, Springer-Verlag, Berlin 1978. MR 58:1332
  • 3. M. A. Krasnoselskii, P. P. Zabreiko, Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Berlin 1984. MR 85b:47057
  • 4. R. Ortega, A boundedness result of Landesman - Lazer type, Differential and Integral Equations, 8 (1995), 729--734. CMP 95:05
  • 5. G. Reuter, Boundedness theorems for nonlinear differential equations of the second order (II), J. London Math. Soc., 27 (1952), 48-58. MR 13:844b
  • 6. N. Rouche, J. Mawhin, Equations Differentielles Ordinaires, Masson, Paris 1973. MR 58:1318b
  • 7. A. Tineo, An iterative scheme for the N-competing species problem, J. Diff. Eq. 116 (1995), 1--15.
  • 8. J. R. Ward, Asymptotic conditions for periodic solutions of ordinary differential equations, Proc Amer Math Soc, 81 (1981), 415-420. MR 82a:34057
  • 9. J. R. Ward, A topological method for bounded solutions of nonautonomous ordinary differential equations, Trans. Am. Math. Soc.,333 (1992), 709-720. MR 93b:34046
  • 10. T. Yoshizawa, Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Springer-Verlag, New York 1975. MR 57:6673

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34B15, 34C11

Retrieve articles in all journals with MSC (1991): 34B15, 34C11


Additional Information

Rafael Ortega
Affiliation: Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
Email: rortega@goliat.ugr.es

Antonio Tineo
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de los Andes, 5101-Mérida, Venezuela
Email: atineo@ciens.ula.ve

DOI: https://doi.org/10.1090/S0002-9939-96-03457-0
Received by editor(s): January 18, 1995
Communicated by: Hal L. Smith
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society