具有时滞的非线性积分方程振动性的研究

Research of oscillatory solution of a kind of nonlinear integral equation with time delay

研究了具有时滞的非线性积分方程振动性问题， 给出了方程 ｘ （ｔ）＋∫ｔ０ｋ（ｔ－ ｓ） Ｇ（ｓ，ｘ（ｓ），ｘ （ｓ－ τ（ｓ）））ｄｓ＝ ｆ （ｔ）在非线性项 Ｇ（ｔ，ｕ，ｖ）关于 ｕ，ｖ 为增函数时，其解振动的充分条件及当强迫项 ｆ（ｔ）为振动函数时。

The sufficient conditions of oscillatory solution are given for integral equation x(t)+∫ t 0k(t-s)G(s,x(s),x(s-τ(s))) d s=f(t), with nonlinear term G(t,u,v) being increment function about u,v . And the sufficient conditions of unbounded solution are given with forced term f(t) being oscillatory function.