Galewski, Marek Stability of solutions for an abstract Dirichlet problem. (English) Zbl 1097.47053 Ann. Pol. Math. 83, No. 3, 273-280 (2004). Summary: 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. Cited in 7 Documents MSC: 47J05 Equations involving nonlinear operators (general) 35A15 Variational methods applied to PDEs 34D20 Stability of solutions to ordinary differential equations 35J20 Variational methods for second-order elliptic equations 35J60 Nonlinear elliptic equations Keywords:stability; semilinear Dirichlet problem; superquadratic nonlinearity PDFBibTeX XMLCite \textit{M. Galewski}, Ann. Pol. Math. 83, No. 3, 273--280 (2004; Zbl 1097.47053) Full Text: DOI