BOUNDEDNESS AND CONVERGENCE FOR THE NON-LINARD TYPE DIFFERENTIAL EQUATION

【摘要】 <正>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.更多还原

【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.更多还原