Department Of Mathematics, Kansas State University
| WEDNESDAY Nov. 18 : | Analysis Seminar |
| Title: | Implicit function theorem via the Dynamical Systems Method (DSM) |
| A.G. Ramm
The Dynamical Systems Method (DSM) for solving a class of nonlinear operator equations F (u) = f in a Hilbert space H is discussed. Sufficient conditions are given for an implicit function theorem to hold. The result is established by an application of the version of the Dynamical Systems Method (DSM), a Newton-type method. This result allows one to solve the above equations in the case when the Frechet derivative F'(u) of the nonlinear operator F is a smoothing operator, so that its inverse is an unbounded operator. The DSM version we discuss is: u(t) = -[F'(u(t)]^-1 (F(u(t)) - f ), u(0) = u_0 . Under suitable assumptions we prove that a) the above problem has a global solution, b) there exists u(\infty),and c) F (u(\infty)) = f. | |
| Time and Place: | 4:30 PM Cardwell 120 |