Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian

We consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal...

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Main Author:	Dorota Bors
Format:	Article
Language:	English
Published:	Hindawi Limited 2014-01-01
Series:	The Scientific World Journal
Online Access:	http://dx.doi.org/10.1155/2014/920537

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spelling	doaj-20d4bb61adce4946ae8bb7fd296df09c2020-11-24T22:26:09ZengHindawi LimitedThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/920537920537Stability of Nonlinear Dirichlet BVPs Governed by Fractional LaplacianDorota Bors0Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, PolandWe consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem.http://dx.doi.org/10.1155/2014/920537
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Dorota Bors
spellingShingle	Dorota Bors Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian The Scientific World Journal
author_facet	Dorota Bors
author_sort	Dorota Bors
title	Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian
title_short	Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian
title_full	Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian
title_fullStr	Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian
title_full_unstemmed	Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian
title_sort	stability of nonlinear dirichlet bvps governed by fractional laplacian
publisher	Hindawi Limited
series	The Scientific World Journal
issn	2356-6140 1537-744X
publishDate	2014-01-01
description	We consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem.
url	http://dx.doi.org/10.1155/2014/920537
work_keys_str_mv	AT dorotabors stabilityofnonlineardirichletbvpsgovernedbyfractionallaplacian
_version_	1725754500298309632

Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian

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