Iterative method for solutions and coupled quasi-solutions of nonlinear Fredholm integral equations in ordered Banach spaces
The paper is concerned with new existence theorems of solutions and of coupled minimal and maximal quasi-solutions for nonlinear Fredholm integral equations by means of monotone iterative techniques. The purpose of this paper is to establish some new existence theorems on maximal and minimal solutions for integral equations in ordered Banach spaces, when the function under the integral does not possess any monotone assumption like in earlier work of \textit{D. Guo} [Northeast. Math. J. 7, No. 4, 416-423 (1991; Zbl 0755.45024)]. For preparing the main results, 5 lemmas are stated. The results obtained are applied to two-point boundary value problems of second-order nonlinear ordinary differential equations in ordered Banach spaces and to an infinite system of nonlinear integral equations of a particular form.
second-order nonlinear ordinary differential equations
infinite system of nonlinear integral equations
scientific article; zbMATH DE number 955225