Continuous Dependence of the Solutions of Eluptic Bwnoary Value Problems on the Coefficients, Right Hand Sides and Boundary Conditions

Kok, B.J.; Penning, F D

doi:10.1080/16073606.1981.9631870

Cited by 5 publications

(1 citation statement)

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“…In this work sufficient conditions for stability of the linear partial differential equation defined in the classical spaces of smooth solutions were formulated. Analogous results for the scalar linear partial differential equation with the Dirichlet boundary conditions defined on the Sobolev spaces were proved in the paper [ 48 ]. The results on the stability of multidimensional nonlinear boundary value problems with variable parameters appeared in papers [ 49 – 51 ] where ordinary differential equations with two-point boundary conditions and variable functional parameters were investigated, and the stability conditions with respect to the strong and weak topology were proved.…”

Section: Discussionmentioning

confidence: 75%

Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian

Bors

2014

The Scientific World Journal

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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.

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Section: Discussionmentioning

confidence: 75%