Elliptic differential-operator problems with a spectral parameter in both the equation and boundary-operator conditions

Abstract

We consider boundary value problems for elliptic differential-operator equations with the spectral parameter and operator-boundary conditions containing a parameter of the same order as the equation. An isomorphism and the corresponding estimate of a solution (with respect to the space variable and the parameter) are obtained. Then, discreteness of the spectrum and completeness of a system of root functions of the corresponding homogeneous problem are established. Finally, an application is given of the abstract results obtained on the isomorphism and the completeness to boundary value problems for elliptic differential equations with a parameter in non-smooth domains.