The solution methods of operator equations with variation methods on hilbert spaces

In this study applying of variation methods of given operator equations on Hilbert spaces and approximate solving methods wieved. Than conditionally extremum problem discussed. İn here for second order derivative Linear diferantial equation and for Laplace and Poisson equations linear boundary value problems reduced variation problems. Using Ritz method finding methods of approximate solves of second order derivative Linear diferantial equation, Schturm-Liouville boundary value problem, Dirichlet problem for laplace eqation, wieved. In final chapter given operator equations which are on real and complex hilbert space discussed reducing to equivalent variation problems, finding methods of approximate solves wieved using Ritz method.