SOLVABILITY OF BOUNDARY VALUE PROBLEMS FOR A SECOND ORDER ELLIPTIC DIFFERENTIAL-OPERATOR EQUATION WITH A SPECTRAL PARAMETER IN BOTH THE EQUATION AND BOUNDARY CONDITIONS

In the Hilbert space H we consider a boundary value problem for a second order elliptic differential-operator equation with a spectral parameter and operator-boundary conditions containing a spectral parameter of the some order that in the equation. Isomorphism and appropriate estimation of the solution (with respect to space variable and parameter) are obtained, discreteness of spectrum and completeness of a system of root functions of appropriate homogeneous problem is established. In conclusion we give applications of abstract results for obtaining isomophism and completeness of boundary value problems for elliptic differential equations with a parameter in non-smooth domains.