scholarly journals Multiple Solutions for a Sixth Order Boundary Value Problem

2021 ◽  
Vol 22 (1) ◽  
pp. 1-12
Author(s):  
A. L. M. Martinez ◽  
C. A. Pendeza Martinez ◽  
G. M. Bressan ◽  
R. M. Souza ◽  
E. W. Stiegelmeier
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Order Equation ◽  
Sixth Order ◽  
Contraction Principle ◽  
Banach’S Contraction Principle

This work presents conditions for the existence of multiple solutions for a sixth order equation with homogeneous boundary conditions using Avery Peterson's theorem. In addition, non-trivial examples are presented and a new numerical method based on the Banach's Contraction Principle is introduced.  

scholarly journals Boundary value problem with integral conditions for a linear third-order equation

2003 ◽  
Vol 2003 (11) ◽  
pp. 553-567 ◽  
Author(s):  
M. Denche ◽  
A. Memou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Order Equation ◽  
Integral Conditions ◽  
Third Order ◽  
Integral Boundary

We prove the existence and uniqueness of a strong solution for a linear third-order equation with integral boundary conditions. The proof uses energy inequalities and the density of the range of the generated operator.

Compatibility Equations in the Theory of Elasticity

2003 ◽  
Vol 125 (2) ◽  
pp. 244-245 ◽  
Author(s):  
Igor V. Andrianov ◽  
Jan Awrejcewicz
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Sixth Order ◽  
Operational Method ◽  
Equilibrium Equations ◽  
Additional Boundary Conditions

It is shown by operational method that the boundary value problem of the theory of elasticity related to stresses, which can be reduced to three strains compatibility equations and to three equilibrium equations, in fact is of sixth order. Hence, it is not required to formulate additional boundary conditions.

scholarly journals Existence of a unique positive solution for a singular fractional boundary value problem

2018 ◽  
Vol 34 (1) ◽  
pp. 57-64
Author(s):  
E. T. KARIMOV ◽  
◽  
K. SADARANGANI ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Fractional Order ◽  
Boundary Value ◽  
Order Equation ◽  
Fractional Boundary Value Problem ◽  
Unique Positive Solution

In the present work, we discuss the existence of a unique positive solution of a boundary value problem for a nonlinear fractional order equation with singularity. Precisely, order of equation Dα 0+u(t) = f(t, u(t)) belongs to (3, 4] and f has a singularity at t = 0 and as a boundary conditions we use... Using a fixed point theorem, we prove the existence of unique positive solution of the considered problem.

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

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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