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 = del g(u) by assuming that L.: D(L) subset of H --> H (H - a Hilbert space) is self-adjont, with a closed range, and g: H --> R is continuous convex on H and Gateaux 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 u + au = DuF(t, u, omega), t epsilon[0,pi] a.e., with the Dirichlet boundary conditions u(0) = u(pi) = 0, where a greater than or equal to 1, and omega is a functional parameter. (C) 2000 Academic Press.