Bounded and almost automorphic solutions of a Liénard equation with a singular nonlinearity

P. Cieutat, Université Versailles-Saint-Quentin-en-Yvelines, Versailles cedex, France
S. Fatajou, Université de Cadi Ayyad, Marrakech, Morocco
G. M. N'Guérékata, Morgan State University, E. Cold Spring Lane, Baltimore, MD, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 21. (2008), pp. 1-15.

Communicated by S. Murakami. Received on 2008-02-03
Appeared on 2008-05-25

Abstract: We study some properties of bounded and $C^{(1)}$-almost automorphic solutions of the following Li\'enard equation: $$x'' + f(x)x' + g(x) = p(t) $$, where $p : {\bf R} \longrightarrow {\bf R}$ is an almost automorphic function, $f$, $g : (a,b) \longrightarrow {\bf R}$ are continuous functions and $g$ is strictly decreasing.

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