Proceedings of the American Mathematical Society

Author(s): Rafael Ortega; Antonio Tineo
Journal: Proc. Amer. Math. Soc. 124 (1996), 2089-2096.
MSC (1991): Primary 34B15, 34C11
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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.

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

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

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: 10.1090/S0002-9939-96-03457-0
PII: S 0002-9939(96)03457-0
Received by editor(s): January 18, 1995
Communicated by: Hal L. Smith
Copyright of article: Copyright 1996, American Mathematical Society

J. Mawhin,Bounded solutions of nonlinear ordinary differential equations,Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations (Udine, Italy), CISM Courses and Lectures,vol. 371, Springer, Vienna, 1996, pp. 121-147.

A. Fonda, F. Zanolin, Bounded solutions of nonlinear second order ordinary differential equations,Discrete and Continuous Dynamical Systems 4(1998), 91-98. (english)

J. Mawhin, J. Ward, Bounded solutions of some second order nonlinear differential equations, J. London Math. Soc. 58 (1998), 733-747.

J.M. Alonso, J. Mawhin, R. Ortega, Bounded solutions of second order semilinear evolution equations and applications to the telegraph equation, J. Math. Pures Appl. 78 (1999), 49-63.

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