Boundedness and convergence for the non-Liénard type differential equation*

In this article, the author studies the boundedness and convergence for the non—Liénard type differential equation {x0=a(y)-f(x),y0=b(y)β(x)-g(x)+e(t),where a(y), b(y), f(x), g(x), β(x) are real continuous functions in y ∈ R or x ∈ R, β(x)≥0 for all x and e(t) is a real continuous function on R+= {t: t≥0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended.