ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A FIRST AND SECOND-ORDER DISCRETE BOUNDARY VALUE PROBLEM


Coskun A. E. , DEMİR A.

JOURNAL OF MATHEMATICAL ANALYSIS, cilt.11, ss.86-101, 2020 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 11 Konu: 2
  • Basım Tarihi: 2020
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS
  • Sayfa Sayıları: ss.86-101

Özet

To purpose of the first part of this paper is to study the nonlinear first order discrete boundary value problem subjected to two-point boundary condition. We establish a new sufficient condition for the existence and uniqueness of the nonlinear first order difference evolution equation. The existence and uniqueness of solutions are proven by means of Banach contraction principle. We define an iteration procedure and apply our results to show that iterated solutions converge to the solutions of the discrete problem. We prove the iteration procedure is terminated when the residual is acceptably small. To illustrate the existence of a unique solution of the contraction mapping theorem some examples are included. In the second part of this study, we consider the following second-order difference boundary value problem