TY  - EJOU
AU  - 
T1  - A Simple Criterion for the Non-Existence of Limit Cycles of a Lienard System
T2  - International Journal of Mathematical Research

PY  - 2016
VL  - 5
IS  - 2
SN  - 2306-2223

AB  - In this paper, as an application in our results, the non-existence of limit cycles for the Liénard system  x ̇ = y –F (x), y ̇=-g(x)  with F (x)=(x^2-x) e^(-x)  (x≥-1)  and 5(x^2+x) e^(x+2)+2e (x≤-1),g(x)=x is discussed by the simple criterion. Graef [1] in 1971 has studied the uniformly boundedness of the solution orbits under the condition (C1) and further proved the existence of limit cycles under the conditions (C1) and (C2) . Recently, Cioni and Villari [2] in 2015 gave the same result as in Graef [1] under the conditions (C1) and (C3) includes (C2). Our aim is to discuss on the case of which (C1) is satisfied, but (C3) is not satisfied. As the result, we shall give the simple criterion for the non-existence of limit cycles for a Liénard system with these conditions. 
KW  - Liénard system
KW  - Limit cycles
KW  - Globa l unstability
KW  - Non-existence
KW  - Homoclinic orbits
KW  - Uniformly boundedness.
DO  - 10.18488/journal.24/2016.5.2/24.2.119.122