Theory of Differential Inequalities for Two-Point Boundary Value Problems and their Applications to Three-Point B.V.Ps Associated with n th Order Non-Linear System of Differential Equations

2002 ◽  
Vol 81 (1) ◽  
pp. 39-49 ◽  
Author(s):  
K.N. Murty ◽  
G.V.R.L. Sarma
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Differential Inequalities ◽  
Point Boundary ◽  
System Of Differential Equations ◽  
Non Linear ◽  
Non Linear System

Matrix boundary-value problems for differential equations with p-Laplacian

2020 ◽  
Vol 17 (1) ◽  
pp. 41-57
Author(s):  
Olga Nesmelova
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Arbitrary Function ◽  
Algebraic System ◽  
Boundary Value ◽  
System Of Differential Equations ◽  
Differential Algebraic System ◽  
Uniqueness Of The Solution

We consider the boundary-value problem for a linear system of differential equations with matrix p-Laplacian, which is reduced to the traditional differential-algebraic system with an unknown in the form of the vector function. A generalization of various boundary-value problems for differential equations with p-Laplacian, which preserves the features of the solution of such problems, namely, the lack of uniqueness of the solution and, in this case, the dependence of the desired solution on an arbitrary function, is given.

scholarly journals Uniqueness intervals and two–point boundary value problems

2009 ◽  
Vol 43 (1) ◽  
pp. 91-97
Author(s):  
Grant B. Gustafson
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Graphical Representation ◽  
Boundary Value ◽  
Conjugate Function ◽  
Point Boundary ◽  
System Of Differential Equations ◽  
Linear Homogeneous Differential Equation

Abstract Consider a linear nth order differential equation with continuous coefficients and continuous forcing term. The maximal uniqueness interval for a classical 2-point boundary value problem will be calculated by an algorithm that uses an auxiliary linear system of differential equations, called a Mikusinski system. This system always has higher order than n. The algorithm leads to a graphical representation of the uniqueness profile and to a new method for solving 2-point boundary value problems. The ideas are applied to construct a graphic for the conjugate function associated with the nth order linear homogeneous differential equation. Details are given about how to solve classical 2-point boundary value problems, using auxiliary Mikusinski systems and Green’s function.

scholarly journals THEORY OF DIFFERENTIAL INEQUALITIES ASSOCIATED WITH $n$th ORDER NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS TO THREE POINT BOUNDARY VALUE PROBLEMS

1998 ◽  
Vol 29 (2) ◽  
pp. 137-144
Author(s):  
K. N. MURTHY ◽  
C. V. RAO
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Differential Inequalities ◽  
Point Boundary ◽  
Uniqueness Of Solutions

Differential inequalities are used as a tool to establish uniqueness of solutions to three point boundary value problems associated with nth order nonlinear differential equations.

scholarly journals On nonlinear discontinuous two-point boundary value problems for third order differential equations

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 185-197
Author(s):  
M.S.N. Murty ◽  
Suresh Kumar
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Extremal Solutions ◽  
Differential Inequalities ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Third Order

In this paper we prove existence of weak extremal solutions for third order nonlinear discontinuous two-point boundary value problems. Further, we obtain two weak differential inequalities for proving boundedness and uniqueness of solutions of related boundary value problems. .

scholarly journals Bilateral approximations and periodic solutions of systems of differential equations with impulses

1985 ◽  
Vol 31 (2) ◽  
pp. 293-307
Author(s):  
S.G. Hristova ◽  
D.D. Bainov
Keyword(s):  
Periodic Solution ◽  
Linear System ◽  
Differential Equations ◽  
Periodic Solutions ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Non Linear ◽  
Impulsive Perturbations ◽  
Non Linear System

The paper justifies a method of bilateral approximations for finding the periodic solution of a non-linear system of differential equations with impulsive perturbations at fixed moments of time.

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