The unique solution of boundary value problems for nonlinear second-order integral-differential equations of mixed type in Banach spaces
Integral-differential equations of the form \[ -u''(t)=f(t,u(t),Tu(t),Su(t)),\qquad t\in[0,1] \] are considered, where \[ (Tu)(t)=\int_0^1 k(t,s)u(s)ds, \quad (Su)(t)=\int_0^1 h(t,s)u(s)ds \] with continuous \(h,k\), Banach space valued \(u\), Banach space valued \(f\). Under some order conditions, the existence of a unique solution is shown by an iteration process.
scientific article; zbMATH DE number 5288029