Existence and uniqueness of solutions for the system of integro-differential equations with three-point and nonlinear integral boundary conditions - Mardanov, M.J.; Sharifov, Y.A.; Ismayilova, K.E. (Bulletin of the Karaganda University. Mathematics Series, 2020)
The paper examines a system of nonlinear integro-differential equations with three-point and nonlinear integral boundary conditions. The original problem demonstrated to be equivalent to integral equations by using Green function. Theorems on the existence and uniqueness of a solution to the boundary value problems for the first order nonlinear system of integro- differential equations with three-point and nonlinear integral boundary conditions are proved. A proof of uniqueness theorem of the solution is obtained by Banach fixed point principle, and the existence theorem then follows from Schaefer’s theorem.