Affiliation:
1. Baku Engineering University , Khirdalan city, 120, AZ0102, Absheron, Baku, Azerbaijan .
Abstract
Abstract
In the present paper, we study a system of nonlinear differential equations with three-point boundary conditions. The given original problem is reduced to the equivalent integral equations using Green function. Several theorems are proved concerning the existence and uniqueness of solutions to the boundary value problems for the first order nonlinear system of ordinary differential equations with three-point boundary conditions. The uniqueness theorem is proved by Banach fixed point principle, and the existence theorem is based on Schafer’s theorem. Then, we describe different types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability. We discuss the stability results providing suitable example.
Reference35 articles.
1. [1] R. E. Bellman, Stability Theory of Differential Equations, McGraw-Hill, New York, Toronto, London, 1953.
2. [2] C. Bucur and E. Valdinoci, Nonlocal Diffusion and Applications, vol. 20 of Lecture Notes of the Unione Matematica Italiana, Springer, Basel, 2016.
3. [3] L. P. Castro and A. M. Simŏes, Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of Hammerstein integral equations, Amer.Inst. Phys, AIP Conf. Proc.1798(1) (2017), 020036, 10 pages.
4. [4] S. Şevgin and H. Şevli, Stability of a nonlinear Volterra integro-differential equation via a fixed point approach, J. Nonlinear Sci.Appl.9 (2016), 200–207.
5. [5] S. M. Ulam, Problems in Modern Mathematics, John Wiley and Sons, New York, 1940.