On the Dirichlet Problem for a Second Order Elliptic System with Degeneration on the Entire Domain Boundary

1999 ◽  
Vol 6 (4) ◽  
pp. 395-400
Author(s):  
M. Usanetashvili
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Elliptic System ◽  
Domain Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Entire Domain ◽  
Order Elliptic System

Abstract The solvability of the first boundary value problem is investigated for a second order elliptic system with degeneration on the entire domain boundary.

On the Dirichlet Problem for a Second Order Elliptic System with Degeneration on the Whole Boundary of a Multidimensional Domain

2008 ◽  
Vol 15 (4) ◽  
pp. 793-798
Author(s):  
Mikheil Usanetashvili
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Elliptic System ◽  
Boundary Value ◽  
Second Order ◽  
Entire Boundary ◽  
Order Elliptic System ◽  
Multidimensional Domain

Abstract The solvability of the first boundary value problem is studied for a second order elliptic system with degeneration on the entire boundary of a multidimensional domain.

One method for the boundary value problem eigenvalues calcuating for a second-order differential equation with a fractional derivative

2019 ◽  
Vol 10 (01) ◽  
pp. 1941004
Author(s):  
Temirkhan Aleroev ◽  
Hedi Aleroeva ◽  
Lyudmila Kirianova
Keyword(s):  
Differential Equation ◽  
Perturbation Theory ◽  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Second Order ◽  
Linear Operators

In this paper, we give a formula for computing the eigenvalues of the Dirichlet problem for a differential equation of second-order with fractional derivatives in the lower terms. We obtained this formula using the perturbation theory for linear operators. Using this formula we can write out the system of eigenvalues for the problem under consideration.

scholarly journals On unique solvability of a Dirichlet problem with nonlinearity depending on the derivative

2019 ◽  
Vol 39 (2) ◽  
pp. 131-144
Author(s):  
Michał Bełdziński ◽  
Marek Galewski
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Unique Solvability ◽  
Existence And Uniqueness ◽  
Variational Approach ◽  
Boundary Value ◽  
Uniqueness Result ◽  
Second Order

In this work we consider second order Dirichelet boundary value problem with nonlinearity depending on the derivative. Using a global diffeomorphism theorem we propose a new variational approach leading to the existence and uniqueness result for such problems.

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