On Volterra integral equations with weakly singular kernels in Banach spaces
On Volterra integral equations with weakly singular kernels in Banach spaces
复制标题
Banach空间中弱奇异核的Volterra积分方程
DOI：
10.1515/dema-1993-0114
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发表时间：
1993
影响因子：
2
通讯作者：
J. Januszewski
中科院分区：
文献类型：
--
作者：
J. Januszewski
Let E, F be Banach spaces, D=[0,d1] x...x [0,dn] and D(t) = {s=(s1,...,sn)eR : Oss^st.^, i=l,...,n> for t=(t1#...,tn)eD. In this paper we prove the existence of a solution and we study the structure of the solution set of the integral equation (1) x(t)=g(t) + S A(t,s)f(s,x(s))ds, D(t) where: 1° g : D —» E is a continuous function; 2° (t,x) —> f(t,x) is a function from DxE into F, which is continuous in x , strongly measurable in t and ||f(s,x)|| s M^ for seD, ||x|| s h; 3° A(t,s) = s ) t o < r < n (t*s), where H is a continuous It-sl* 2 . . function from D into the space of continuous linear mappings F —» E. Denote by a the Kuratowski measure of noncompatness. For a given set V of functions from D into E we define a function v by v(t) = a (V(t)) for teD, where V(t) = {x(t) : xeV}. Before passing to further considerations we shall quote two lemmas. Lemma 1. ([3], L.39.2) If o
