scholarly journals Kronecker Product of matrices and their applications to self-adjoint two-point boundary value problems associated with first order matrix differential systems

2021 ◽  
Vol 10 (10) ◽  
pp. 25399-25407
Author(s):  
Sriram Bhagavatula ◽  
Dileep Durani Musa ◽  
Murty Kanuri
Keyword(s):  
Boundary Value Problems ◽  
Kronecker Product ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Least Square ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Differential Systems ◽  
First Order ◽  
Product Of Matrices

In this paper, we shall be concerned with Kronecker product or Tensor product of matrices and develop their properties in a systematic way. The properties of the Kronecker product of matrices is used as a tool to establish existence and uniqueness of solutions to two-point boundary value problems associated with system of first order differential systems. A new approach is described to solve the Kronecker product linear systems and establish best least square solutions to the problem. Several interesting examples are given to highlight the importance of Kronecker product of matrices. We present adjoint boundary value problems and deduce a set of necessary and sufficient conditions for the Kronecker product boundary value problem to be self-adjoint.

scholarly journals A Peek into Theory of Automation with Applications to Various Branches of Science

2020 ◽  
Vol 9 (09) ◽  
pp. 25156-25160
Author(s):  
Divyalaxmi N.
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Least Square ◽  
Uniqueness Of Solution ◽  
Characteristic Matrix ◽  
Point Boundary ◽  
Difference System ◽  
Lattice Vector ◽  
First Order

In this paper, we shall be concerned with the existence and uniqueness of solution to three- point boundary value problems associated with a system of first order matrix difference system. Shortest and Closest Lattice vector methods are used as a tool to obtain the best least square solution of the  three-point boundary value problems when  the characteristic matrix D is rectangular. In this paper, we shall be concerned with the existence and uniqueness of solution to three- point boundary value problems associated with a system of first order matrix difference system. Shortest and Closest Lattice vector methods are used as a tool to obtain the best least square solution of the  three-point boundary value problems when  the characteristic matrix D is rectangular. 

scholarly journals Generalized two point boundary value problems. existence and uniqueness

1992 ◽  
Vol 5 (2) ◽  
pp. 147-156
Author(s):  
K. N. Murty ◽  
S. Sivasundaram
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Pseudo Inverse

An algorithm is presented for finding the pseudo-inverse of a rectangular matrix. Using this algorithm as a tool, existence and uniqueness of solutions to two point boundary value problems associated with general first order matrix differential equations are established.

scholarly journals Solvability of Three-Point Boundary Value Problems at Resonance with ap-Laplacian on Finite and Infinite Intervals

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Hairong Lian ◽  
Patricia J. Y. Wong ◽  
Shu Yang
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Term ◽  
Order Differential Equation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
First Order ◽  
At Resonance ◽  
Infinite Intervals

Three-point boundary value problems of second-order differential equation with ap-Laplacian on finite and infinite intervals are investigated in this paper. By using a new continuation theorem, sufficient conditions are given, under the resonance conditions, to guarantee the existence of solutions to such boundary value problems with the nonlinear term involving in the first-order derivative explicitly.

On Two-Point Boundary Value Problems for Two-Dimensional Differential Systems with Singularities

2003 ◽  
Vol 10 (3) ◽  
pp. 595-602
Author(s):  
S. Mukhigulashvili
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Two Dimensional ◽  
Point Boundary ◽  
Differential Systems

Abstract For a differential system where λ ∈]0, 1[ and ℎ𝑖 :]𝑎, 𝑏[×]0, +∞[×ℝ → [0, +∞[ (𝑖 = 0, 1, 2) are continuous functions, we have established sufficient conditions for the existence of at least one solution satisfying one of the two boundary conditions and

scholarly journals First-Order Three-Point Boundary Value Problems at Resonance Part III

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Mesliza Mohamed ◽  
Bevan Thompson ◽  
Muhammad Sufian Jusoh
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Implicit Function Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Implicit Function ◽  
Point Boundary ◽  
First Order ◽  
At Resonance

The main purpose of this paper is to investigate the existence of solutions of BVPs for a very general case in which both the system of ordinary differential equations and the boundary conditions are nonlinear. By employing the implicit function theorem, sufficient conditions for the existence of three-point boundary value problems are established.

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

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