Reflecting function and solutions of two-point boundary value problems for nonautonomous two-dimensional differential systems

2012 ◽  
Vol 48 (1) ◽  
pp. 147-152 ◽  
Author(s):  
E. V. Varenikova
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Two Dimensional ◽  
Point Boundary ◽  
Differential Systems ◽  
Reflecting Function

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 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.

A priori estimates of solutions of boundary value problems for two-dimensional systems of singular differential inequalities

2011 ◽  
Vol 18 (1) ◽  
pp. 163-175
Author(s):  
Nino Partsvania
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Differential Inequalities ◽  
Two Dimensional ◽  
Point Boundary ◽  
Estimates Of Solutions ◽  
Priori Estimates ◽  
Singular Coefficients

Abstract A priori estimates of solutions of two-point boundary value problems for two-dimensional systems of differential inequalities with singular coefficients are established.

scholarly journals Existence Results and the Monotone Iterative Technique for Nonlinear Fractional Differential Systems with Coupled Four-Point Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yujun Cui ◽  
Yumei Zou
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Point Boundary ◽  
Differential Systems ◽  
Monotone Iterative ◽  
Fractional Differential Systems ◽  
Fractional Differential

By establishing a comparison result and using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence of solutions for nonlinear fractional differential systems with coupled four-point boundary value problems.

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