A Note on Bounded Solutions of a Generalized Lienard Type System

Juan E. Nápoles Valdes, Luciano M. Lugo Motta Bittencurt


In this paper we study the boundedness of solutions of some generalized Liénard type system under non usual conditions on evolved functions using the Second Method of Lyapunov.


Boundedness; asymptotic behavior; Liénard equation Type .

Full Text:



Liapunov, A. M. Probléme général de la stabilité du movement, in Annals of Math. Studies No.17, Princeton Univ. Press, Princeton, NJ, 1949.

Antosiewicz, H. A. A survey of Lyapunov´s second method contributions to the theory of nonlinear oscillations IV in Annals of Math. Studies No.44, Princeton Univ. Press, Princeton, NJ, 1958.

Barbashin, E. A. Lyapunov´s Functions, Science Publishers, Moscow, 1970 (Russian).

Cesari, L. Asymptotic behavior and stability problems in ordinary differential equations, Springer-Verlag, Berlin, 1959.

Demidovich, B. P. Lectures on the Mathematical Theory of the Stability, Science Publishers, Moscow, 1967 (Russian).

Hahn, W. Theory and Application of Liapunov´s Direct Method, Prentice-Hall, Englewood Cliffs, New Jersey, 1963.

Yoshizawa, T. Stability theory by Liapunov´s second method, The Mathematical Society of Japan, 1966.

Liénard, A. Étude des oscillations entreteneus, Revue Génerale de l´Électricité 23: 901-912, 946-954 (1928).

Van der Pol, B. On oscillation hysteresis in a triode generator with two degrees of freedom, Phil. Mag (6) 43, 700-719 (1922).

Van der Pol, B. On “relaxation-oscillations”, Philosophical Magazine, 2(11): 978-992, 1926.

Guckenheimer, J. and P. Holmes. Nonlinear ascillations, dynamical systems, and bifurcations of vector fields, volume 42 of Applied Mathematical Sciences. Springer-Verlag, New York, 2002. Revised and corrected reprint of the 1983 original.

Hricisakova, D. Continuability and (non-) oscillatory properties of solutions of generalized Lienard equation, Hiroshima Math. J. 20 (1990), 11-22.


  • There are currently no refbacks.




About ASRJETS | Privacy PolicyTerms & Conditions | Contact Us | DisclaimerFAQs 

ASRJETS is published by (GSSRR).