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Dwi Susanti
Mathematics Department, Faculty Mathematics and Natural Sciences, Universitas Padjajaran Bandung, Indonesia
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Some Properties of Green’s Matrix of Nonlinear Boundary Value Problem of First Order Differential Badrulfalah Badrulfalah; Dwi Susanti; Kafsah Joebaedi; Robin Kosasih
EKSAKTA: Berkala Ilmiah Bidang MIPA Vol. 20 No. 1 (2019): Eksakta : Berkala Ilmiah Bidang MIPA (E-ISSN : 2549-7464)
Publisher : Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Negeri Padang, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (957.931 KB) | DOI: 10.24036/eksakta/vol20-iss1/173

Abstract

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.
Co-Authors Badrulfalah Badrulfalah Kafsah Joebaedi Robin Kosasih