Monotone iterative technique for nonlinear boundary-value problem of first-order differential systems with rectangular coefficients

Some Properties of Green’s Matrix of Nonlinear Boundary Value Problem of First Order Differential

“…( ) is called in column space of ( ) ∈ ℝ × if there exist some matrix ( ) ∈ ℝ × a such that ( ) = ( ) ( ) for every . [9] Consider an equation = ,…”

“…The least square solution of (1.3) is = + with + = ( ) −1 where > . [9] The following Lemma 1.4 give a boundary value problem that equivalent to (1.1), (1.2).…”

“…The difference follow the form of differential equations or regarded variable [2,5,6,7]. In the other side in [9] , it has been proved uniqueness the solution of nonlinear boundary value problem of firstorder differential system with rectangular coefficients by using method of iterative monotone.…”

“…Inspired by [2,5,6,7,9], in this research will be discussed the property of the Green's function that hold on the Green's matrix of nonlinear boundary value problem of first-order differential system with rectangular coefficients. The objective of this research is to prove that the Green's matrix and the assosiated generalized Green's matrix of the relevant boundary value problem satisfy the property of Green's function.…”

A Solution of Nonlinear Boundary Value Problem of System With Rectangular Coefficients

“…The uniqueness of the solution is found by using the property of uniqueness of Moore-Penrose generalized inverse. In [10] it has been proved the uniqueness of solution the boundary value problem ( ), ( ) by using Monotone Iterative Technique. Based on [3,8,10], we will give an alternative proving of that problem ( ), ( ) by using fixed point theorem of contractive mapping.…”