Geodesic
Stability of solutions for an abstract Dirichlet problem
Marek Galewski1
1 Faculty of Mathematics University of Łódź Banacha 22 90-238 Łódź, Poland
Annales Polonici Mathematici, Tome 83 (2004) no. 3, pp. 273-280.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider continuous dependence of solutions on the right hand side for a semilinear operator equation $Lx=\nabla G( x) $, where $L:D( L) \subset Y\rightarrow Y$ ($Y$ a Hilbert space) is self-adjoint and positive definite and $G:Y\rightarrow Y$ 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.
DOI : 10.4064/ap83-3-9
Keywords: consider continuous dependence solutions right side semilinear operator equation nabla where subset rightarrow hilbert space self adjoint positive definite rightarrow convex functional superquadratic growth applications derive stability results dependence functional parameter fourth order dirichlet problem applications given

Marek Galewski 1

1 Faculty of Mathematics University of Łódź Banacha 22 90-238 Łódź, Poland 
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Marek Galewski. Stability of solutions for an abstract Dirichlet problem. Annales Polonici Mathematici, Tome 83 (2004) no. 3, pp. 273-280. doi : 10.4064/ap83-3-9. http://geodesic.mathdoc.fr/articles/10.4064/ap83-3-9/

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