Positive solutions and asymptotic behavior of delay differential equations with nonlinear impulses

[摘要] Consider the delay differential equation (DDE) with nonlinear impulses x(t) + Sigma(i=1)(n)p(i)(t)x(t-tau(i)) = 0, t not equal t(j), t greater than or equal to t(0), x(t(j)(+)) - x(t(j)) = I-j(x(t(j))), j = 1,2,..., (*) where p(i) is an element of C([t(0),infinity),R(+)), tau(i) greater than or equal to 0 for i = 1,2,...,n, and I-j is an element of C(R,R) for j = 1,2,.... The purpose of this paper is to obtain a necessary and sufficient condition for the existence of positive solutions of DDE without impulses and to establish a kind of order persistence of solutions of Eq. (*) and criteria of the asymptotic behavior of Eq. (*), which can be used to improve and develop some of the known results in the literature. (C) 1997 Academic Press.

[发布日期] 1997-03-15