Open AccessConditions for the existence of smooth solutions for a class of fourth order operator-differential equations
Author(s) -
А. Р. Алиев,
N. L. MURADOVA
Publication year - 2022
Publication title -
baku mathematical journal
Language(s) - English
Resource type - Journals
eISSN - 2790-8429
pISSN - 2790-8410
DOI - 10.32010/j.bmj.2022.01
Subject(s) - mathematics , sobolev space , operator (biology) , connection (principal bundle) , mathematical analysis , differential equation , semi elliptic operator , class (philosophy) , order (exchange) , differential operator , pure mathematics , computer science , biochemistry , chemistry , geometry , finance , repressor , artificial intelligence , transcription factor , economics , gene
. In the paper, we consider a fourth-order operator-differential equation on the entire axis, the main part of which has a multiple characteristic, and we introduce the concept of its ”smoothly” regular solvability. We find exact values of the norms of intermediate derivatives operators in a Sobolev-type space and indicate their connection with the conditions for the solvability of the equation under study. Note that the conditions found for ”smoothly” regular solvability are sufficient and are imposed only on the operator coefficients of the operator-differential equation under consideration