scholarly journals Important Notes for a Fuzzy Boundary Value Problem

2019 ◽  
Vol 4 (2) ◽  
pp. 305-314 ◽  
Author(s):  
Hülya Gültekin Çitil
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Boundary Value ◽  
Liouville Problem ◽  
Eigenvalue Parameter ◽  
Sturm Liouville ◽  
Fuzzy Boundary

AbstractIn this paper is studied a fuzzy Sturm-Liouville problem with the eigenvalue parameter in the boundary condition. Important notes are given for the problem. Integral equations are found of the problem.

scholarly journals Spectral Analysis of -Sturm-Liouville Problem with the Spectral Parameter in the Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Aytekin Eryılmaz
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Spectral Parameter ◽  
Difference Operator ◽  
Boundary Value ◽  
Liouville Problem ◽  
Scattering Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Sturm Liouville ◽  
Spectral Representations

This paper is concerned with -Sturm-Liouville boundary value problem in the Hilbert space with a spectral parameter in the boundary condition. We construct a self-adjoint dilation of the maximal dissipative -difference operator and its incoming and outcoming spectral representations, which make it possible to determine the scattering matrix of the dilation. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of operator generated by boundary value problem.

Factorization Ladders and Eigenfunctions

1949 ◽  
Vol 1 (4) ◽  
pp. 379-396 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Manufacturing Process ◽  
Boundary Value ◽  
Factorization Method ◽  
Sturm Liouville ◽  
The Subject

The eigenfunctions of a boundary value problem are characterized by two quite distinct properties. They are solutions of ordinary differential equations, and they satisfy prescribed boundary conditions. It is a definite advantage to combine these two requirements into a single problem expressed by a unified formula. The use of integral equations is an example in point. The subject of this paper, namely the Schrödinger-Infeld Factorization Method, which is applicable to certain restricted. Sturm-Liouville problems, is based upon another combination of the two properties. The Factorization Method prescribes a manufacturing process.

scholarly journals Note on the conformable boundary value problems: Sturm’s theorems and Green’s function

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 471
Author(s):  
F. Martínez ◽  
I. Martínez ◽  
M. K. A. Kaabar ◽  
S. Paredes
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Boundary Value ◽  
Liouville Problem ◽  
Comparison Theorems ◽  
Conformable Derivative ◽  
Sturm Liouville ◽  
Linear Differential

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

scholarly journals TRANSFORMATION OF STURM–LIOUVILLE PROBLEMS WITH DECREASING AFFINE BOUNDARY CONDITIONS

2004 ◽  
Vol 47 (3) ◽  
pp. 533-552 ◽  
Author(s):  
Paul A. Binding ◽  
Patrick J. Browne ◽  
Warren J. Code ◽  
Bruce A. Watson
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Subject Classification ◽  
Darboux Transformations ◽  
Sturm Liouville

AbstractWe consider Sturm–Liouville boundary-value problems on the interval $[0,1]$ of the form $-y''+qy=\lambda y$ with boundary conditions $y'(0)\sin\alpha=y(0)\cos\alpha$ and $y'(1)=(a\lambda+b)y(1)$, where $a\lt0$. We show that via multiple Crum–Darboux transformations, this boundary-value problem can be transformed ‘almost’ isospectrally to a boundary-value problem of the same form, but with the boundary condition at $x=1$ replaced by $y'(1)\sin\beta=y(1)\cos\beta$, for some $\beta$.AMS 2000 Mathematics subject classification: Primary 34B07; 47E05; 34L05

NODAL SOLUTIONS OF NONLOCAL BOUNDARY VALUE PROBLEMS

2009 ◽  
Vol 14 (4) ◽  
pp. 435-450 ◽  
Author(s):  
John Chamberlain ◽  
Lingju Kong ◽  
Qingkai Kong
Keyword(s):  
Boundary Condition ◽  
Nonlinear Boundary ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Stieltjes Integral ◽  
Nodal Solutions ◽  
Different Types ◽  
Sturm Liouville

We study the nonlinear boundary value problem consisting of the second order differential equation on [a, b] and a boundary condition involving a Riemann‐Stieltjes integral. By relating it to the eigenvalues of a linear Sturm‐Liouville problem with a two‐point separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions of this problem. We also discuss the changes of the existence of different types of nodal solutions as the problem changes.

scholarly journals Note on the Conformable Boundary Value Problems: Sturm’s Theorems and Green’s Function

2020 ◽  
Author(s):  
F. Martínez ◽  
Inmaculada Martínez ◽  
Mohammed K. A. Kaabar ◽  
Silvestre Paredes
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Boundary Value ◽  
Liouville Problem ◽  
Comparison Theorems ◽  
Conformable Derivative ◽  
Sturm Liouville ◽  
Linear Differential

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

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