Uniformly stable solution of a nonlocal problem of coupled system of differential equations

Abstract

Abstract. In this paper we are concerned with a nonlocal problem of a coupled system of differential equations. We study the local existence of the solution and its continuous dependence. The global existence and its uniform stability is being studied.Mathematics subject classification (2010): 34B18, 34B10.

Existence of solution of a coupled system of differential equation with the nonlocal two-point boundary conditions

“…In [ 7] the authors studied the existence of at least one solution of the nonlocal problem with the nonlocal conditions In this system the unknown functions and depend only on with two boundary conditions at multi points in the interval , but in this paper we prove the existence of solutions for a nonlocal problem ( 1)-( 4) in which the unknown functions and depend on functions and of with two boundary conditions at two points in the interval .…”

Solution of Coupled System of Cauchy Problem of Nonlocal Differential Equations E. A. A. Ziada

“…The Cauchy problems with multi-point or non-local conditions have been extensively studied by several authors in the last two decades. The interested reader can see [1]- [13].…”

Continuous dependence of the solution of Ito stochastic differential equation with nonlocal conditions

“…Many authors in the last decades studied nonlocal problems of ordinary differential equations, the reader is referred to [1][2][3][4][5][6][7] , and references therein. Also the theory of stochastic differential equations, random fixed point theory, existence of solutions of stochastic differential equations by using successive approximation method and properties of these solutions have been extensively studied by several authors, especially those contain the Brownian motion as a formal derivative of the Gausian white noise, the Brownian motion W (t), t ∈ R, is defined as a stochastic process such that W (0) = 0; E(W (t)) = 0, E(W (t)) 2 = t and [W (t 1 ) W (t 2 )] is a Gaussian random variable for all t 1 , t 2 ∈ R. The reader is referred to [8,9] and [10][11][12][13][14][15][16] and references therein.…”