THE SET OF SOLUTIONS OF VOLTERRA AND URYSOHN INTEGRAL EQUATIONS IN BANACH SPACES

被引:0
|
作者
Sikorska-Nowak, Aneta [1 ]
机构
[1] Adam Mickiewicz Univ, Fac Math & Comp Sci, PL-61614 Poznan, Poland
关键词
Existence of solution; set of solution; Henstock-Kurzweil integral; Pettis integral; HenstockKurzweilPettis integral; nonlinear Volterra integral equation; nonlinear Urysohn integral equation; measures of weak noncompactness; ORDINARY DIFFERENTIAL-EQUATIONS; THEOREMS;
D O I
10.1216/RMJ-2010-40-4-1313
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove to existence theorems of solutions of nonlinear integral equations of Uryshohn type x(t) = phi(t) + lambda integral(alpha)(0) f(t, s, x(s)) ds and Volterra type x(t) = phi(t) + integral(t)(0) f(t, s, x(s)) ds, t is an element of I-alpha = [0, alpha], alpha, lambda is an element of R-+,R- with the Henstock-Kurzweil-Pettis integral. Moreover, we show that the set S of all solutions of the Volterra integral equation is compact and connected. The assumptions about the function f are really weak: scalar measurability and weak sequential continuity with respect tot the third variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness.
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页码:1313 / 1331
页数:19
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