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

Badrulfalah Badrulfalah (Mathematics Departments, Faculty Mathematics and Natural Sciences, Universitas Padjajaran Bandung, Indonesia)
Dwi Susanti (Mathematics Department, Faculty Mathematics and Natural Sciences, Universitas Padjajaran Bandung, Indonesia)
Kafsah Joebaedi (Mathematics Department, Faculty Mathematics and Natural Sciences, Universitas Padjajaran Bandung, Indoneisa)
Robin Kosasih (Mathematics Department, Faculty Mathematics and Natural Sciences, Universitas Padjajaran Bandung, Indonesia)

Eksakta : Berkala Ilmiah Bidang MIPA
Vol. 20 No. 1 (2019): Eksakta : Berkala Ilmiah Bidang MIPA (E-ISSN : 2549-7464)

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.