On a Class of Time Inhomogeneous Nonsingular Flows and Schrödinger Operators.
On -differentiable Fredholm operators of nonstationary initial-boundary value problems
We are dealing with Dirichlet, Neumann and Newton type initial-boundary value problems for a general second order nonlinear evolution equation. Using the Fredholm operator theory we establish some sufficient conditions for Fréchet differentiability of associated operators to the given problems. With help of these results the generic properties, existence and continuous dependency of solutions for initial-boundary value problems are studied.
On the asymptotic behaviour of a solution of a differential equation in a Hilbert space