Search

Start Over Subject periodic problem

1. Localization of nonsmooth lower and upper functions for periodic boundary value problems

Creator:
Rachůnková, Irena and Tvrdý, Milan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
second order nonlinear ordinary differential equation, periodic problem, lower and upper functions, and generalized linear differential equation
Language:
English
Description:
In this paper we present conditions ensuring the existence and localization of lower and upper functions of the periodic boundary value problem u '' + k u = f(t, u), u(0) = u(2 π), u 0 (0) = u 0 (2π), k ∈ R, k ≠ 0. These functions are constructed as solutions of some related generalized linear problems and can be nonsmooth in general.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On solvability sets of boundary value problems for linear functional differential equations

Creator:
Bravyi, Eugene
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
functional differential equation, boundary value problem, and periodic problem
Language:
English
Description:
Consider boundary value problems for a functional differential equation ( x (n) (t) = (T +x)(t) − (T −x)(t) + f(t), t ∈ [a, b], lx = c, where T +, T − : C[a, b] → L[a, b] are positive linear operators; l: ACn−1 [a, b] → R n is a linear bounded vector-functional, f ∈ L[a, b], c ∈ ℝ n , n ≥ 2. Let the solvability set be the set of all points (T +, T −) ∈ ℝ + 2 such that for all operators T +, T − with kT ±kC→L = T ± the problems have a unique solution for every f and c. A method of finding the solvability sets are proposed. Some new properties of these sets are obtained in various cases. We continue the investigations of the solvability sets started in R. Hakl, A. Lomtatidze, J. Šremr: Some boundary value problems for first order scalar functional differential equations. Folia Mathematica 10, Brno, 2002.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Resonance and multiplicity in periodic boundary value problems with singularity

Creator:
Rachůnková, Irena, Tvrdý, Milan, and Vrkoč, Ivo
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
second order nonlinear ordinary differential equation, periodic problem, and lower and upper functions
Language:
English
Description:
The paper deals with the boundary value problem u '' + k u = g(u) + e(t), u(0) = u(2π), u ' (0) = u ' (2π), where k ∈ R, g : (0, ∞) → R is continuous, e ∈ L[0, 2π] and lim x→0+ ∫1 x g(s) ds = ∞. In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public