On solution of delay boundary value problems.

The main objective of this thesis could be divided into two main aspects, which are: 1. Studying and solving boundary eigenvalue problems without deviating arguments and its generalization to boundary eigenvalue problems with deviating arguments. 2. Evaluating the variational formulation of the delay BVPS, using two approaches (variational problem with constraint and variational problem using Rayleigh quotient formula), as well as, the equivalence between the solution of the original problem in operator form Ly=f and the variational problem have been proved. Several examples of boundary eigenvalue problems are considered to explain the realistic of the variational approach used in this thesis.