\documentstyle[12pt]{article} \begin{document} \title{ ON THE VARIATIONAL ASPECTS FOR ELLIPTIC PROBLEMS WITH PARAMETER ON THE BOUNDARY \author{ Andrey B. Andreev and Assen H. Hristov} \date{} \maketitle \begin{abstract} We consider a class of second order elliptic equations with a parameter in the domain as well as on the boundary. This is a general kind of the eigenvalue problem for elliptic operator. The conditions when the spectrum is real are presented. The corresponded variational eigenvalue problems in weak formulation are discussed. The problems considered in this paper are referred to the Galerkin approximations of the Steklov-type eigenvalue problems. \end{abstract} Andrey B. Andreev\\ Department of Mathematics,\\ Technical University of Gabrovo,\\ Bulgaria\\ $\&$ Central Laboratory for Parallel Processing,\\ Bulgarian Academy of Sciences, Sofia, \\ e-mail: Andreev@Copern.Acad.BG.\\ \newline Assen H. Hristov\\ Department of Geometry,\\ University of Plovdiv,\\ str."Tsar Assen"1,\\ Plovdiv,BULGARIA\\ e-mail: asehri@uni-plovdiv.bg \end{document}