Three-point boundary value problems for singular system of first order differential equations

Abstract

In this paper we prove existence and uniqueness results to three point boundary value problems associated with singular system of first order differential equations by the use of generalized inverses of matrices.

Moore-Penrose Generalized Inverse to Kronecker Product Matrix Boundary Value Problems

“…The importance of system of differential equations and their occurrence in many physical problems are well known. Many authors [ [4]- [6]& [11]] have studied the problems of existence-uniqueness to two and 3-point boundary value problems(BVP's) for the first order matrix system of differential equations.…”

Three-point boundary value problems for singular system of first order differential equations

“…M y(a) + N y(b) + Ry(c) = 0 (4) has only the trivial solution. Generalized inverse of a matrix is used as a tool to study the existence and uniqueness criteria of (1) and (2). Several authors [2], [5] have studied existence and uniqueness of solutions to two and three point boundary value problems associated with the system (1), when P is non-singular.…”

“…Generalized inverse of a matrix is used as a tool to study the existence and uniqueness criteria of (1) and (2). Several authors [2], [5] have studied existence and uniqueness of solutions to two and three point boundary value problems associated with the system (1), when P is non-singular. Recently Murty and Rao [3] obtained existence and uniqueness criteria to two point boundary value problems associated with the system (1) with the help of generalized inverses.…”

“…Section 3 deals with obtaining existence and uniqueness criteria to three point boundary value problems associated with (1) satisfying (2). Some properties of the related Green's matrices are also studied.…”