Abstract and Applied Analysis
Volume 2007 (2007), Article ID 51410, 27 pages
doi:10.1155/2007/51410
Degenerate differential operators with parameters
Veli B. Shakhmurov
Department of Electrical-Electronics Engineering, Faculty of Engineering, Istanbul University, Avcilar 34320, Istanbul, Turkey
Abstract
The nonlocal boundary value problems for regular degenerate differential-operator equations with the parameter are studied. The principal parts of the appropriate generated differential operators are non-self-adjoint. Several conditions for the maximal regularity uniformly with respect to the parameter and the Fredholmness in Banach-valued Lp− spaces of these problems are given. In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.