ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34, 47 Idczak, Dariusz, University of d, Poland Stability in semilinear problems In the paper, we derive results concerning a continuous dependence of solutions on the right-hand side for a semilinear operator equation Lu = ∇g(u), by assuming that L : D(L) ⊂ H → H (H−a Hilbert space) is self-adjont, with a closed range, and g : H → R is continuous convex on H and Gâteaux differentiable on D(L). Using these results, we obtain theorems on the continuous dependence of solutions on functional parameters for a semilinear problem of the second order ü + au = D_{u}F (t, u, ω), t ∈ [0, π] a.e., with the Dirichlet boundary conditions u(0) = u(π) = 0, where a ≥ 1, and ω is a functional parameter.