Nonlocal elliptic problems with a parameter

An elliptic equation with a parameter in a domain $Q$ with smooth boundary $\Gamma$, and boundary conditions relating the values of the function and its derivatives on $\Gamma$ with their values on a compact set $\omega\subset Q$ ($ \omega\cap\Gamma=\varnothing$), is studied, along with analogous problems on a cylinder. A priori estimates of solutions are obtained. The existence of a unique solution of the boundary value problem is proved for a sufficiently large parameter.
Bibliography: 16 titles.