On the existence and uniqueness of an R ν-generalized solution of a boundary value problem with uncoordinated degeneration of the input data

2014 ◽  
Vol 90 (2) ◽  
pp. 562-564 ◽  
Author(s):  
V. A. Rukavishnikov
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Input Data ◽  
Boundary Value ◽  
Generalized Solution

scholarly journals On the Existence and Uniqueness ofRv-Generalized Solution for Dirichlet Problem with Singularity on All Boundary

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
V. Rukavishnikov ◽  
E. Rukavishnikova
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Input Data ◽  
Generalized Solution ◽  
Two Dimensional ◽  
Order Elliptic Equation ◽  
Second Order Elliptic Equation ◽  
Dimensional Domain

The existence and uniqueness of theRv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.

scholarly journals On one problem with dynamic nonlocal condition for ahyperbolic equation

2017 ◽  
Vol 21 (3) ◽  
pp. 44-52
Author(s):  
A.E. Savenkova
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Input Data ◽  
Nonlocal Condition ◽  
Generalized Solution ◽  
Embedding Theorems ◽  
Hyperbolic Partial Differential Equation ◽  
Apriori Estimates

In this article, boundary value problem for hyperbolic partial differential equation with nonlocal data in an integral of the second kind form is considered. The emergence of dynamic conditions may be due to the presence of a damping device. Existence and uniqueness of generalized solution is proved in a given cylindrical field. There is some limitation on the input data. The uniqueness of generalized solution is proved by apriori estimates. The existence is proved by Galerkin’s method and embedding theorems.

scholarly journals On Differential Properties Rν-Generalized Solution of the Dirichlet Problem with Coordinated Degeneration of the Input Data

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Victor Anatolievich Rukavishnikov
Keyword(s):  
Differential Equation ◽  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Input Data ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Generalized Solution ◽  
Strong Singularity ◽  
Second Order Differential Equation ◽  
Differential Properties

We consider the first boundary value problem for second-order differential equation with strong singularity caused by coordinated degeneration of the input data. For this problem, we study the differential properties of the Rν-generalized solution, that is, the fact that it belongs to the space H2,ν+β/2k+2(Ω).

scholarly journals On One Damping Problem for a Nonstationary Control System with Aftereffect

2019 ◽  
Vol 65 (4) ◽  
pp. 547-556
Author(s):  
A. S. Adkhamova ◽  
A. L. Skubachevskii
Keyword(s):  
Control System ◽  
Boundary Value Problem ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Neutral Type ◽  
Generalized Solution ◽  
Matrix Coefficients ◽  
Nonlocal Functional ◽  
Several Delays

We consider a control system described by the system of differential-difference equations of neutral type with variable matrix coefficients and several delays. We establish the relation between the variational problem for the nonlocal functional describing the multidimensional control system with delays and the corresponding boundary-value problem for the system of differential-difference equations. We prove the existence and uniqueness of the generalized solution of this boundary-value problem.

scholarly journals ON A BOUNDARY VALUE PROBLEM WITH NONLOCAL IN TIME CONDITIONS FOR A ONE-DIMENSIONAL HYPERBOLIC EQUATION

2017 ◽  
Vol 19 (6) ◽  
pp. 31-39
Author(s):  
S.V. Kirichenko
Keyword(s):  
Initial Data ◽  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Form ◽  
Generalized Solution ◽  
One Dimensional

In this article, the boundary value problem for hyperbolic equation with nonlocal initial data in integral form is considered. Existence and uniqueness of generalized solution are proved.

scholarly journals Existence and uniqueness of solutions for a mixed p-Laplace boundary value problem involving fractional derivatives

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuqi Wang ◽  
Zhanbing Bai
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Novel Approach ◽  
Banach Contraction ◽  
Left And Right ◽  
Banach Contraction Mapping Principle

AbstractIn this article, the existence and uniqueness of solutions for a multi-point fractional boundary value problem involving two different left and right fractional derivatives with p-Laplace operator is studied. A novel approach is used to acquire the desired results, and the core of the method is Banach contraction mapping principle. Finally, an example is given to verify the results.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

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