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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.1 Antofagasta Mar. 2016 

Proyecciones Journal of Mathematics Vol. 35, No 1, pp. 41-61, March 2016. Universidad Católica del Norte Antofagasta - Chile

Sufficient conditions for the boundedness and square integrability of Solutions of fourth-order differential equations

Moussadek Remili

Mebrouk Rahmane

University of Oran 1



Sufficient conditions for the boundedness and square integrability of solutions and their derivatives of certain fourth order nonlin-ear differential equation are given by means of the Lyapunov’s second method. Our results obtained in this work, generalize existing results on fourth order nonlinear differential equations in the literature. For illustration, an example is also given.

2010 Mathematics Subject Classification : 34C11.

Keywords and phrases :    Boundedness,    stability, Lyapunov functional, fourth-order differential equations, square integrable.


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Moussadek Remili

Department of Mathematics University of Oran 1 Ahmed Ben Bella 31000 Oran Algeria

e-mail :

Mebrouk Rahmane

Department of Mathematics University of Oran 1 Ahmed Ben Bella 31000 Oran Algeria

e-mail :

Received : March 2015. Accepted : November 2015

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