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


This paper discusses Green’s matrix of nonlinear boundary value problem of first-order differential system with rectangular coeffisients, especially about its properties. In this case, the differential equation of the form  with boundary conditions of the form   and  which  is a real  matrix with  whose entries are continuous on  and . ,  are nonsingular matrices such that  and  are constant vectors. To get the Green’s matrix and the assosiated generalized Green’s matrix, we change the boundary condition problem into an equivalent  differential equation by using the properties of the  Moore-Penrose generalized inverse, then  its solution is found by using method of variation of parameters. The last we prove  that the defined matrices  satisfy the properties of green’s function. The result is the corresponding the Green’s matrix and the assosiated generalized Green’s matrix have the property of Green’s functions with the jump-discontinuity.