MEASURABLE SOLUTIONS OF IMPLICIT INTEGRAL EQUATIONS WITH DISCONTINUOUS RIGHT-HAND SIDE

被引：0

作者：

Cubiotti, Paolo ^{[1
]}

机构：

[1] Univ Messina, Dept Math & Comp Sci, Phys Sci & Earth Sci, Viale F Stagno dAlcontres 31, I-98166 Messina, Italy

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2018年 / 19卷 / 02期

关键词：

Integral equations; discontinuity; discontinuous selections; operator inclusions;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove an existence theorem for measurable solutions u : [a, b] -> Y of the integral equation psi(t, u(t)) = phi(t, integral(t)(a) h(s, u(s)) ds), where Y is a compact, connected and locally connected metric space, and h : [a, b] x Y -> R-n, psi : [a, b] x Y -> R and phi : [a, b] x R-n -> R are given functions. Our result extends and improves a previous result, valid for the case where n = 1 and psi does not depend on t explicitly. A function phi : [a, b] x R-n -> R satisfying our assumptions can be discontinuous (with respect to the second variable) even at all points x is an element of R-n.

引用

页码：207 / 217

页数：11