Existence and uniqueness of the solution of boundary-value problems for integrodifferential equations of superneutral type

1977 ◽  
Vol 28 (4) ◽  
pp. 419-424
Author(s):  
T. St. Nikolova ◽  
D. D. Bainov
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integrodifferential Equations ◽  
Uniqueness Of The Solution

scholarly journals ON THE SOLVABILITY OF SOME BOUNDARY VALUE PROBLEMS WITH INVOLUTION

2020 ◽  
Vol 26 (3) ◽  
pp. 7-16
Author(s):  
K. Zh. Nazarova ◽  
B. Kh. Turmetov ◽  
K. I. Usmanov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Laplace Operator ◽  
Poisson Equation ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Boundary Operator ◽  
Uniqueness Of The Solution ◽  
The Laplace Operator

This article is devoted to the study of the solvability of some boundary value problems with involution.In the space Rn, the map Sx=x is introduced. Using this mapping, a nonlocal analogue of the Laplace operator is introduced, as well as a boundary operator with an inclined derivative. Boundary-value problems are studied that generalize the well-known problem with an inclined derivative. Theorems on the existence and uniqueness of the solution of the problems under study are proved. In the Helder class, the smoothness of the solution is also studied. Using well-known statements about solutions of a boundary value problem with an inclined derivative for the classical Poisson equation, exact orders of smoothness of a solution to the problem under study are found.

scholarly journals Fractional boundary value problems: Analysis and numerical methods

2011 ◽  
Vol 14 (4) ◽  
Author(s):  
Neville Ford ◽  
M. Morgado
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Uniqueness Of The Solution ◽  
Fractional Boundary Value Problems

AbstractIn this paper we consider nonlinear boundary value problems for differential equations of fractional order α, 0 < α < 1. We study the existence and uniqueness of the solution and extend existing published results. In the last part of the paper we study a class of prototype methods to determine their numerical solution.

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.

scholarly journals Existence and uniqueness criteria for the higher-order Hilfer fractional boundary value problems at resonance

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yousef Gholami
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Higher Order ◽  
Coupled Systems ◽  
At Resonance ◽  
Uniqueness Criteria ◽  
Fractional Boundary Value Problems

Abstract This investigation is devoted to the study of a certain class of coupled systems of higher-order Hilfer fractional boundary value problems at resonance. Combining the coincidence degree theory with the Lipschitz-type continuity conditions on nonlinearities, we present some existence and uniqueness criteria. Finally, to practically implement the obtained theoretical criteria, we give an illustrative application.

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