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Erratum to the paper "A note on stability of solutions for abstract semilinear dirichlet problems"

Galewski M.

Journal of Applied Analysis

2007

Vol. 13, nr 2

303-304

A note on stability of solutions for abstract semilinear Dirichlet problems

Galewski M

Journal of Applied Analysis

2006

Vol. 12, nr 1

71-81

We provide stability results for the family Lκu=∇Fκ(u) where Lκ is positive definite and selfadjoint operator and ∇Fκ for κ=0,1,2,... is a gradient mapping. The abstract results obtained are applied to prove the stability and continuous dependence on parameters for the fourth order Dirichlet problems for ordinary differential equations with the differential operator depending on numerical parameters.

Remark on the abstract Dirichlet problem for Baire-one functions

Kalenda O. F. K.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 1

55-73

We study the possibility of extending any bounded Baire-one function on the set of extreme points of a compact convex set to an affine Baire-one function and related questions. We give complete solutions to these questions within a class of Choquet simplices introduced by P. J. Stacey (1979). In particular we get an example of a Choquet simplex such that its set of extreme points is not Borel but any bounded Baire-one function on the set of extreme points can be extended to an affine Baire-one function. We also study the analogous questions for functions of higher Baire classes.