Stability of solutions for an abstract Dirichlet problem

Tom 83 / 2004

Marek Galewski Annales Polonici Mathematici 83 (2004), 273-280 MSC: 47J05, 35A15. DOI: 10.4064/ap83-3-9


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.


  • Marek GalewskiFaculty of Mathematics
    University of Łódź
    Banacha 22
    90-238 Łódź, Poland

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