We consider continuous dependence of solutions on the right hand side for a semilinear operator equation Lx = ∇G(x), where L: D(L) ⊂ Y → Y (Y a Hilbert space) is self-adjoint and positive definite and G:Y → Y is a convex functional with superquadratic growth. As applications we derive some stability results and dependence on a functional parameter for a fourth order Dirichlet problem. Applications to P.D.E. are also given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-3-9,
author = {Marek Galewski},
title = {Stability of solutions for an abstract Dirichlet problem},
journal = {Annales Polonici Mathematici},
volume = {83},
year = {2004},
pages = {273-280},
zbl = {1097.47053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-3-9}
}
Marek Galewski. Stability of solutions for an abstract Dirichlet problem. Annales Polonici Mathematici, Tome 83 (2004) pp. 273-280. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-3-9/