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1. Continuous dependence of solutions of generalized linear ordinary differential equations on a parameter

Creator:
Halas, Zdeněk
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
generalized linear ordinary differential equations, fundamental matrix, continuous dependence on a parameter, and emphatic convergence
Language:
English
Description:
We present here the problem of continuous dependence for generalized linear ordinary differential equations in the case when uniform convergence is violated. This work continues research of M. Ashordia (1993) and M. Tvrdý (2002).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Positivity of Green's matrix of nonlocal boundary value problems

Creator:
Domoshnitsky, Alexander
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
functional differential equation, nonlocal boundary value problem, positivity of Green's operator, fundamental matrix, and differential inequalities
Language:
English
Description:
We propose an approach for studying positivity of Green’s operators of a nonlocal boundary value problem for the system of n linear functional differential equations with the boundary conditions nixi − ∑n j=1 mijxj = βi , i = 1, . . . , n, where ni and mij are linear bounded ''local” and ''nonlocal” functionals, respectively, from the space of absolutely continuous functions. For instance, nixi = xi(ω) or nixi = xi(0) − xi(ω) and mijxj = ∫ ω 0 k(s)xj(s) ds + ∑nij r=1 cijrxj (tijr) can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity of Green’s operator for auxiliary ''local'' problem which consists of a “close” equation and the local conditions nixi = αi , i = 1, . . . , n.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public