scholarly journals k-component disconjugacy for systems of ordinary differential equations

1986 ◽  
Vol 9 (2) ◽  
pp. 373-380
Author(s):  
Johnny Henderson
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Continuous Dependence ◽  
Variational Equation ◽  
Order System ◽  
Differentiability Of Solutions

Disconjugacy of thekth component of themth order system ofnth order differenttal equationsY(n)=f(x,Y,Y′,…,Y(n−1)), (1.1), is defined, wheref(x,Y1,…,Yn),∂f∂yij(x,Y1,…,Yn):(a,b)×Rmn→Rmare continuous. Given a solutionY0(x)of (1.1),k-component disconjugacy of the variational equationZ(n)=∑i=1nfYi(x,Y0(x),…,Y0(n−1)(x))Z(i−1), (1.2), is also studied. Conditions are given for continuous dependence and differentiability of solutions of (1.1) with respect to boundary conditions, and then intervals on which (1.1) isk-component disconjugate are characterized in terms of intervals on which (1.2) isk-component disconjugate.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

scholarly journals A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

2021 ◽  
Vol 11 (11) ◽  
pp. 4798
Author(s):  
Hari Mohan Srivastava ◽  
Sotiris K. Ntouyas ◽  
Mona Alsulami ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Arbitrary Domain ◽  
Banach Contraction ◽  
Coupled Boundary Conditions ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.

Factorization Ladders and Eigenfunctions

1949 ◽  
Vol 1 (4) ◽  
pp. 379-396 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Manufacturing Process ◽  
Boundary Value ◽  
Factorization Method ◽  
Sturm Liouville ◽  
The Subject

The eigenfunctions of a boundary value problem are characterized by two quite distinct properties. They are solutions of ordinary differential equations, and they satisfy prescribed boundary conditions. It is a definite advantage to combine these two requirements into a single problem expressed by a unified formula. The use of integral equations is an example in point. The subject of this paper, namely the Schrödinger-Infeld Factorization Method, which is applicable to certain restricted. Sturm-Liouville problems, is based upon another combination of the two properties. The Factorization Method prescribes a manufacturing process.

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