Solutions of the variational equation for an n-th order boundary value problem with an integral boundary condition

2021 ◽  
Vol 14 (1) ◽  
pp. 155-166
Author(s):  
Benjamin L. Jeffers ◽  
Jeffrey W. Lyons
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Variational Equation ◽  
Boundary Value ◽  
Integral Boundary Condition ◽  
Integral Boundary

scholarly journals An Approximate Grid Solution of a Nonlocal Boundary Value Problem with Integral Boundary Condition for Laplace's Equation

2018 ◽  
Vol 22 ◽  
pp. 01016 ◽  
Author(s):  
Adıgüzel A. Dosiyev ◽  
Rifat Reis
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Condition ◽  
Unknown Boundary ◽  
Laplace’S Equation ◽  
Nonlocal Boundary Value Problem ◽  
Integral Boundary ◽  
Laplace's Equation

A new method for the solution of a nonlocal boundary value problem with integral boundary condition for Laplace's equation on a rectangular domain is proposed and justified. The solution of the given problem is defined as a solution of the Dirichlet problem by constructing the approximate value of the unknown boundary function on the side of the rectangle where the integral boundary condition was given. Further, the five point approximation of the Laplace operator is used on the way of finding the uniform estimation of the error of the solution which is order of 0(h2), where hi s the mesh size. Numerical experiments are given to support the theoretical analysis made.

scholarly journals CLASSICAL SOLUTION FOR INITIAL–BOUNDARY VALUE PROBLEM FOR WAVE EQUATION WITH INTEGRAL BOUNDARY CONDITION

2012 ◽  
Vol 17 (3) ◽  
pp. 309-329 ◽  
Author(s):  
Victor Korzyuk ◽  
Victor Erofeenko ◽  
Julia Sheika
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Boundary Value Problem ◽  
Classical Solution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Integral Boundary Condition ◽  
Integral Boundary ◽  
Initial Boundary Value

The unique existence of classical solution of initial–boundary value problem for wave equation with a special integral boundary condition is proved in the work. Classical solution of the problem in analytical form is also found in the article. This problem arises at the modeling of electromagnetic fields with arbitrary time dependence when interaction between the field and solids is simulated with impedance boundary conditions.

scholarly journals New results for higher-order Hadamard-type fractional differential equations on the half-line

2021 ◽  
Author(s):  
Tugba Senlik Cerdik ◽  
Fulya Yoruk Deren
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Fractional Integral ◽  
Boundary Value ◽  
Integral Boundary Condition ◽  
Fractional Boundary Value Problem ◽  
Integral Boundary ◽  
Multiplicity Results ◽  
Fractional Differential

The purpose of this paper is to analyze a new kind of Hadamard fractional boundary value problem combining integral boundary condition and multipoint fractional integral boundary condition on an infinite interval. By the help of the Bai-Ge’s fixed point theorem, multiplicity results of positive solutions are derived for the Hadamard fractional boundary value problem. In the end, to illustrative the main result, an example is also presented.

scholarly journals Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Bing-Wei Niu ◽  
Jian-Ping Sun ◽  
Qiu-Yan Ren
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Integral Boundary Condition ◽  
Third Order ◽  
Integral Boundary

We are concerned with the following third-order boundary value problem with integral boundary condition:  u′′′(t)=f(t,u(t)),  t∈[0,1],  u′(0)=u(1)=0,  u′′(η)+∫αβ‍u(t)dt=0,where1/2<α≤β≤1,  α+β≤4/3, andη∈(1/2,α]. Although the corresponding Green's function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions onfby using the two-fixed-point theorem due to Avery and Henderson. An example is also included to illustrate the main results obtained.

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