Existence theorems and periodic solutions of neutral integral equations

被引：10

作者：

Burton, TA

Furumochi, T

机构：

[1] NW Res Inst, Port Angeles, WA 98362 USA

[2] Shimane Univ, Dept Math, Matsue, Shimane 6908504, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2001年 / 43卷 / 04期

关键词：

neutral integral equations; periodic solutions; existence theorems;

D O I：

10.1016/S0362-546X(99)00217-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The equations x(t) = a(t)+∫0t D(t,s,x(s))ds+∫t∞ E(t,s,x(s))ds, t∈R+ and x(t) = a(t)+∫∞t D(t,s,x(s))ds+∫t∞ E(t,s,x(s))ds, t∈R, where R+=[0,∞), R=(-∞,∞), a:R→Rn, D:Δ-×Rn→Rn, and E:Δ+×Rn→Rn are continuous, and where Δ-={(t,s):s≤t} and Δ+={(t,s):s≥t} were studied. It is supposed that a(t) is bounded on R+ or a(t) is bounded on R and that for any J>0 there are continuous functions DJ:Δ→R+ and EJ:Δ+→R+ such that |D(t,s,x)|≤DJ(t,s) if ((t,s)∈Δ and |x|≤J, where |·| denotes the Euclidean norm on Rn, |E(t,s,x)|≤EJ(t,s) if (t,s)∈Δ+ and |x|≤J.

引用

页码：527 / 546

页数：20