Banach空间Hammerstein方程L^P—解的存在性

THE EXISTENCE OF L^P—SOLUTIONS ON HAMMERSTEIN EQUATION IN BANACH SPACE

讨论了方程 X(t)=f(t)+λintegral from n=D K(t,S)g(s,x(s))ds x∈D解的存在性,借助于对非紧性测度有关不等式的推广,解决了[1]中提出的问题。

This paper studied the existence of solutions for x(t)=f(t)+λ integral from n=D K(t, s)g(s, x(s))ds x∈D in [1], Szufla wondered if the assumption of noncompactness for g(t, x)could be replaced by the common assumption of noncompactness, this problem is soled.