On an abstract boundary value problem with the eigenvalue parameter in the boundary condition

2000 ◽  
pp. 257-266
Author(s):  
Anatolii Ětkin
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Eigenvalue Parameter ◽  
Abstract Boundary

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 Wellposedness of Neumann boundary-value problems of space-fractional differential equations

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Hong Wang ◽  
Danping Yang
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Neumann Boundary Condition ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Fractional Differential ◽  
Neumann Boundary Value Problems ◽  
Well Posed

AbstractFractional differential equation (FDE) provides an accurate description of transport processes that exhibit anomalous diffusion but introduces new mathematical difficulties that have not been encountered in the context of integer-order differential equation. For example, the wellposedness of the Dirichlet boundary-value problem of one-dimensional variable-coefficient FDE is not fully resolved yet. In addition, Neumann boundary-value problem of FDE poses significant challenges, partly due to the fact that different forms of FDE and different types of Neumann boundary condition have been proposed in the literature depending on different applications.We conduct preliminary mathematical analysis of the wellposedness of different Neumann boundary-value problems of the FDEs. We prove that five out of the nine combinations of three different forms of FDEs that are closed by three types of Neumann boundary conditions are well posed and the remaining four do not admit a solution. In particular, for each form of the FDE there is at least one type of Neumann boundary condition such that the corresponding boundary-value problem is well posed, but there is also at least one type of Neumann boundary condition such that the corresponding boundary-value problem is ill posed. This fully demonstrates the subtlety of the study of FDE, and, in particular, the crucial mathematical modeling question: which combination of FDE and fractional Neumann boundary condition, rather than which form of FDE or fractional Neumann boundary condition, should be used and studied in applications.

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