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Journal of Function Spaces
Volume 2017 (2017), Article ID 2932134, 8 pages
Research Article

On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted Space

1Azerbaijan State Oil and Industry University, 1010 Baku, Azerbaijan
2Institute of Mathematics and Mechanics of ANAS, 1141 Baku, Azerbaijan
3Baku State University, 1148 Baku, Azerbaijan
4Baku Engineering University, Khirdalan City, 0101 Baku, Azerbaijan

Correspondence should be addressed to Sabir S. Mirzoev; ur.liam@ribasveyozrim

Received 30 April 2017; Accepted 27 September 2017; Published 31 October 2017

Academic Editor: Hugo Leiva

Copyright © 2017 Araz R. Aliev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Sufficient conditions are found for the correct and unique solvability of a class of third-order parabolic operator differential equations, whose principal parts have multiple characteristics, in a Sobolev-type space with exponential weight. The estimates for the norms of intermediate derivative operators are obtained and the relationship between these estimates and solvability conditions is established. Besides, the connection is found between the order of exponential weight and the lower bound for the spectrum of abstract operator appearing in the principal part of the equation.