Existence of nonoscillatory solution of second order linear neutral delay equation

[摘要] Consider the neutral delay differential equation with positive and negative coefficients, d(2)/dt(2) [x(t)+px(t - tau)] + Q(1)(t)x(t - sigma(1))- Q(2)(t)x( t - sigma(2)) = 0, where p is an element of R and tau is an element of (0,infinity), sigma(1), sigma(2) is an element of [0, infinity) and Q(1),Q(2) is an element of ([t(0), infinity), R+). Some sufficient conditions for the existence of a nonoscillatory solution of the above equation expressed in terms of integral(infinity) sQ(1)(s) ds < infinity, i =1, 2, and certain technical conditions implying that Q(1)(s) dominates Q(2)(s) are obtained for values of p not equal +/-1. (C) 1998 Academic Press.

[发布日期] 1998-12-15