抽象积分方程解的存在性

The Existence of Solutions of Abstract Integral Equations

考察Banach空间中形如x(t)=integral from N=G(f(t,s,x(s))ds)的非线性积分方程,在f满足一定集压缩性条件的假定下,利用Monch与Darbo的不动点定理证明了上述方程存在取值于给定闭凸集中的连续解.

This paper is concerned with the following nonlinear integral equation in a Banach space X:x(t) = ∫Gf(t,s,x(s))ds ,where G is a compact Hausdorff space with a nonzero regularmeasure μ. Under certain assumptions about the set-contratibility of f,it is proved that the above-mentioned equation has at least one continuous solution which takes its values in some given closed convex subset K of X. The tools used in the paper are two fixed point theorems of Monch and Darbo.