Stability of solutions for an abstract Dirichlet problem
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.