Linear elliptic boundary-value problems with a parameter are studied. The Agranovich-Vishik method and specially introduced function spaces allow us to consider mixed-order problems in unbounded domains. We obtain a priori estimates and unique solvability for large values of the parameter. These results are used to study analytic semi-groups and Fredholm property of general elliptic problems in unbounded domains.
"Elliptic problems with a parameter in unbounded domains." Adv. Differential Equations 12 (5) 573 - 600, 2007.