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THE GENERALISED LIÉNARD EQUATIONS

Published online by Cambridge University Press:  01 September 2009

A. AGHAJANI  and
A. MORADIFAM
A. AGHAJANI
Affiliation:
School of Mathematics, Iran University of Science and Technology, Tehran, Iran e-mail: aghajani@iust.ac.ir
A. MORADIFAM
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver BC, Canada e-mail: a.moradi@math.ubc.ca
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Abstract

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In this paper we present sufficient conditions for all trajectories of the system$\[\dot{x}= \frac{1}{a(x)}[h(y)-F(x)], \ \ \ \ \dot{y}= -a(x)g(x),\]$to cross the vertical isocline h(y) = F(x), which is very important in the global asymptotic stability of the origin, oscillation theory and existence of periodic solutions. Also we give sufficient conditions for all trajectories which start at a point on the curve h(y) = F(x), to cross the y-axis which is closely connected with the existence of homoclinic orbits, stability of the zero solution, oscillation theory and the centre problem. The obtained results extend and improve some of the authors' previous results and some other theorems in the literature.

Keywords

34C3734D0534C05

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 605 - 617
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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