scholarly journals On a Nonlocal Boundary Value Problem for Second Order Nonlinear Singular Differential Equations

2000 ◽  
Vol 7 (1) ◽  
pp. 133-154 ◽  
Author(s):  
A. Lomtatidze ◽  
L. Malaguti
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Bounded Variation ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
Carathéodory Conditions ◽  
Uniqueness Of A Solution

Abstract Criteria for the existence and uniqueness of a solution of the boundary value problem are established, where ƒ :]a, b[×R 2 → R satisfies the local Carathéodory conditions, and μ : [a, b] → R is the function of bounded variation. These criteria apply to the case where the function ƒ has nonintegrable singularities in the first argument at the points a and b.

scholarly journals On second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 56 (1) ◽  
pp. 143-153 ◽  
Author(s):  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problem ◽  
Bounded Variation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

Abstract This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem $$\matrix{{x'' = f(t,x),} \hfill & {x'(0) = 0,} \hfill & {x'(1) = {\int_0^1 {x(s)dg(s)},} }} $$ where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation.

scholarly journals ONE-VALUED SOLVABILITY OF A NONLOCAL PROBLEM FOR THE AXISYMMETRIC HELMHOLTZ EQUATION

2017 ◽  
Vol 17 (2) ◽  
pp. 5-14
Author(s):  
A.A. Abashkin
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Problem ◽  
Degenerate Elliptic Equation ◽  
Nonlocal Boundary Value Problem ◽  
Degenerate Elliptic ◽  
Uniqueness Of A Solution

A nonlocal boundary value problem for degenerate elliptic equation is considered. Boundary value of this problem considerably depend on low derivativecoefficient changes. Existence and uniqueness of a solution are proved.

scholarly journals On a nonlocal boundary value problem for the equation fourth-order in partial derivatives

2021 ◽  
pp. 16-23
Author(s):  
О.Ш. Киличов
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Problem ◽  
Order Equation ◽  
Nonlocal Boundary Value Problem ◽  
Fourth Order Equation ◽  
Uniqueness Of A Solution

В данной статье изучается нелокальная задача для уравнения четвертого порядка в которой доказывается существование и единственность решения этой задачи. Решение построено явно в виде ряда Фурье, обоснованы абсолютная и равномерная сходимость полученного ряда и возможность почленного дифференцирования решения по всем переменным. Установлен критерий однозначной разрешимости поставленной краевой задачи. In this article, we study a nonlocal problem for a fourth-order equation in which the existence and uniqueness of a solution to this problem is proved. The solution is constructed explicitly in the form of a Fourier series; the absolute and uniform convergence of the obtained series and the possibility of term-by-term differentiation of the solution with respect to all variables are substantiated. A criterion for the unique solvability of the stated boundary value problem is established.

Existence results for a second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 53 (1) ◽  
pp. 42-52
Author(s):  
Katarzyna Szymańska-Dȩbowska
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Existence Results ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

The paper focuses on existence of solutions of a system of nonlocal resonant boundary value problems , where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation. Imposing on the function f the following condition: the limit limλ→∞f(t, λ a) exists uniformly in a ∈ Sk−1, we have shown that the problem has at least one solution.

Inner boundary value problem for fractional diffusion equation

2020 ◽  
Vol 20 (3) ◽  
pp. 14-18
Author(s):  
F.M. Losanova ◽  
Keyword(s):  
Diffusion Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Existence And Uniqueness Theorem ◽  
Nonlocal Boundary Value Problem ◽  
Linear Combinations

In this paper, we prove the existence and uniqueness theorem for a nonlocal boundary value problem for the fractional diffusion equation with boundary conditions presented in the form of linear combinations.

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