Nonlinear eigenvalue problems and Galerkin approximations

Nonlinear Eigenvalue Problems and Galerkin Approximations

with u possibly satisfying additional normalization conditions. I t is our purpose in the present note to describe a way of applying a method of Galerkin type to such problems which works in particular for nonlinear elliptic boundary value problems of variational type. We obtain from it a general theorem on the existence of normalized eigenfunctions for the latter problem, and in the case of T ...

Galerkin Approximations of Nonlinear Optimal Control Problems in Hilbert Spaces

Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we...

Nonlinear Eigenvalue Problems

Heinrich Voss Hamburg University of Technology 115.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115-2 115.2 Analytic matrix functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115-3 115.3 Variational Characterization of Eigenvalues . . . . . . . . 115-7 115.4 General Rayleigh Functionals . . . . . . . . . . . . . . . . . . . ...

Solving nonlinear eigenvalue problems

Galerkin approximations for nonlinear evolution inclusions

In this paper we study the convergence properties of the Galerkin approximations to a nonlinear, nonautonomous evolution inclusion and use them to determine the structural properties of the solution set and establish the existence of periodic solutions. An example of a multivalued parabolic p.d.e. is also worked out in detail.