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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
MathSciNet review: 1342038
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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.

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  • 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

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Additional Information

Rafael Ortega
Affiliation: Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain

Antonio Tineo
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de los Andes, 5101-Mérida, Venezuela

Received by editor(s): January 18, 1995
Communicated by: Hal L. Smith
Article copyright: © Copyright 1996 American Mathematical Society

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