Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

[摘要] We prove existence theorems for the integrodifferential equationx'(t)=f(t,x(t),∫0tk(t,s,x(s))ds),x(0)=x0,t∈Ia=[0,a],a>0, wheref,k,xare functions with values in a Banach spaceEand the integral is taken in the sense of HL.Additionally, the functionsfandksatisfy certain boundary conditions expressed in terms of the measureof noncompactness.

[学科分类] 应用数学