关键词: Boundedness, convergence, differential equation

Abstract:

In this article, the author studies the boundedness and convergence for the non--Lienard type differential equation
x' = a(y)-f(x),
y' =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.

Key words: Boundedness, convergence, differential equation