摘要
本文以非紧致测度为工具,进一步研究了Banaeh空间中非线性Volterra积分方程解的存在性和比较结果,在解的存在性准则中我们取消了核函数的一致连续性这一实质性的条件,在极值解的存在性和比较结果中我们也对以往的结果做了许多改进(参见文[1-4]).
The study of the Volterra integral equations in Banach spaces has attracted much attention in recent years[1-5]. The purpose of this paper is to study further Volterra integral equations in Banach spaces by using noncompact measure. We prove in §3 a existence theorem of solution to Volterra integral equations under the condition of nonlinear set contraction, in which we cancel the essential condition that kernel function is uniform continuous. Thus the results unifies and improves the reults in [1-4]. In §4,we prove the existence of extremal solutions and comparison theorems to Volterra integral equations, which also improves the corresponding results in[1-4].
出处
《数学杂志》
CSCD
北大核心
1989年第2期141-150,共10页
Journal of Mathematics
