SOLUTIONS FOR SINGULAR VOLTERRA INTEGRAL EQUATIONS

被引：0
作者：
Wong, Patricia J. Y. [1 ]
机构：
[1] Nanyang Technol Univ, Sch Elect & Elect Engn, Singapore 639798, Singapore
来源：
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2009年
关键词：
Fixed-sign solutions; singularities; Volterra integral equations; CONSTANT-SIGN SOLUTIONS; SYSTEM; UNIQUENESS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the system of Volterra integral equations u(i)(t) = integral(t)(0) gi(t, s)[Pi(s, u(1)(s), u2(s), ..., u(n)(s)) + Q(i)(s, u(1)(s), u(2)(s), ..., u(n)(s))]ds, t is an element of [0, T], 1 <= i <= n where T > 0 is fixed and the nonlinearities P-i(t, u(1), u(2), ..., u(n)) can be singular at t = 0 and u(j) = 0 where j is an element of {1, 2, ..., n}. Criteria are offered for the existence of fixed-sign solutions (u(1)*, u(2)*, ..., u(n)*) to the system of Volterra integral equations, i.e., theta(i)u(i)*(t) >= 0 for t is an element of [0, 1] and 1 <= i <= n, where theta(i) is an element of {1, -1} is fixed. We also include an example to illustrate the usefulness of the results obtained.
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