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All Journal Eksakta : Berkala Ilmiah Bidang MIPA
Iis Irianingsih
Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Padjadjaran, Bandung, Indonesia
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A Solution of Nonlinear Boundary Value Problem of System With Rectangular Coefficients Badrulfalah Badrulfalah; Iis Irianingsih; Khafsah Joebaedi
EKSAKTA: Berkala Ilmiah Bidang MIPA Vol. 21 No. 1 (2020): 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 (1072.606 KB) | DOI: 10.24036/eksakta/vol21-iss1/217

Abstract

This paper discusses a nonlinear boundary value problem of system with rectangular coefficients of the form with boundary conditions of the form A(t)x' + B(t)x = f(t,x) and which is is a real matrix with whose entries are continuous on the form B1x(to)=a and B2x(T)=b which is A(t) is a real m n matri with m > n matrix with m > n whose entries are continuous on J = [to,T] and f E C[J x Rn, Rn]. B1, B2 are nonsingular matrices such that and are constant vectors, especially about the proof of the uniqueness of its solution. To prove it, we use Moore-Penrose generalized inverse and method of variation of parameters to find its solution. Then we show the uniqueness of it by using fixed point theorem of contraction mapping. As the result, under a certain condition, the boundary value problem has a unique solution.
Co-Authors Badrulfalah Badrulfalah Khafsah Joebaedi