scholarly journals Inverse nodal problem for nonlocal differential operators

2019 ◽  
Vol 50 (3) ◽  
pp. 337-347
Author(s):  
Xin-Jian Xu ◽  
Chuan-Fu Yang
Keyword(s):  
Boundary Condition ◽  
Scattering Theory ◽  
Differential Operators ◽  
Diffusion Processes ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Inverse Nodal Problem ◽  
Nodal Data ◽  
Nodal Problem ◽  
The Given

Inverse nodal problem consists in constructing operators from the given zeros of  their eigenfunctions. The problem of differential operators with nonlocal boundary condition appears, e.g., in scattering theory, diffusion processes and the other applicable fields. In this paper, we consider a class of differential operators with nonlocal boundary condition, and show that the potential function can be determined by nodal data.

scholarly journals Rothe time-discretization method for the semilinear heat equation subject to a nonlocal boundary condition

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Nabil Merazga ◽  
Abdelfatah Bouziani
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Time Discretization ◽  
Neumann Condition ◽  
Integral Boundary ◽  
Semilinear Heat Equation ◽  
Rothe Method ◽  
The Given

This paper is devoted to prove, in a nonclassical function space, the weak solvability of a mixed problem which combines a Neumann condition and an integral boundary condition for the semilinear one-dimensional heat equation. The investigation is made by means of approximation by the Rothe method which is based on a semidiscretization of the given problem with respect to the time variable.

scholarly journals INVERSE NODAL PROBLEM FOR A CLASS OF NONLOCAL STURM‐LIOUVILLE OPERATOR

2010 ◽  
Vol 15 (3) ◽  
pp. 383-392 ◽  
Author(s):  
Chuan-Fu Yang
Keyword(s):  
Boundary Condition ◽  
Dense Subset ◽  
Liouville Problem ◽  
Integral Boundary ◽  
Inverse Nodal Problem ◽  
Classical Boundary Condition ◽  
Classical Boundary ◽  
Sturm Liouville ◽  
Nodal Problem ◽  
The Given

Inverse nodal problem consists in constructing operators from the given nodes (zeros) of their eigenfunctions. In this work, the Sturm‐Liouville problem with one classical boundary condition and another nonlocal integral boundary condition is considered. We prove that a dense subset of nodal points uniquely determine the boundary condition parameter and the potential function of the Sturm‐Liouville equation. We also provide a constructive procedure for the solution of the inverse nodal problem.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

scholarly journals Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Hongliang Gao ◽  
Xiaoling Han
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
The Fixed Point Theorem

By using the fixed point theorem, existence of positive solutions for fractional differential equation with nonlocal boundary conditionD0+αu(t)+a(t)f(t,u(t))=0,0<t<1,u(0)=0,u(1)=∑i=1∞αiu(ξi)is considered, where1<α≤2is a real number,D0+αis the standard Riemann-Liouville differentiation, andξi∈(0,1),  αi∈[0,∞)with∑i=1∞αiξiα-1<1,a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,1]×[0,∞),[0,∞)).

Global Existence and Blow-Up of Solutions for a Porous Medium Equation

2012 ◽  
Vol 461 ◽  
pp. 532-536
Author(s):  
Yun Zhu Gao ◽  
Xi Meng ◽  
Hong Gai
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Global Existence ◽  
Blow Up ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Porous Medium Equation ◽  
Local Source ◽  
Medium Equation ◽  
The Fixed Point Theorem

In this paper, a porous medium equation with local source and nonlocal boundary condition is studied. By using the fixed point theorem and comparison principle. The global existence and blow-up of solutions are obtained .

scholarly journals Global Existence and Decay for a System of Two Singular Nonlinear Viscoelastic Equations with General Source and Localized Frictional Damping Terms

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Salah Mahmoud Boulaaras ◽  
Rafik Guefaifia ◽  
Nadia Mezouar ◽  
Ahmad Mohammed Alghamdi
Keyword(s):  
Boundary Condition ◽  
Lyapunov Functional ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Dimensional System ◽  
One Dimensional ◽  
Nonlinear Viscoelastic ◽  
Frictional Damping ◽  
Viscoelastic Equations ◽  
General Source

The current paper deals with the proof of a global solution of a viscoelasticity singular one-dimensional system with localized frictional damping and general source terms, taking into consideration nonlocal boundary condition. Moreover, similar to that in Boulaaras’ recent studies by constructing a Lyapunov functional and use it together with the perturbed energy method in order to prove a general decay result.

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