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=DuF(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