About kernel of inverse operator L' to third-order derivative's Ly = −y+q(x)y operator

Omer Cakir2025-12-122025-12-122011Omer Cakir /About kernel of inverse operator L' to third-order derivative's Ly = −y+q(x)y operator / Suleyman Demirel University/ СДУ хабаршысы, 2(18).https://repository.sdu.edu.kz/handle/123456789/2333This article investigates the kernel of the inverse operator associated with the third-order differential operator defined by Ly = −y'' + q(x)y under periodic-type boundary conditions. Using Kolmogorov widths and s-number theory, we establish estimates for the operator’s properties and demonstrate that the inverse operator is a kernel operator when q(x) is continuous and satisfies q(x) ≥ 1. Several supporting lemmas are proven, including inequalities for the operator and relationships between s-numbers and Kolmogorov widths. The results provide a theoretical framework for understanding the behavior of higher-order differential operators in Hilbert and Banach spaces.enAttribution-NonCommercial-ShareAlike 4.0 InternationalThird-order differential operatorinverse operatorkernel operatorKolmogorov widthsperiodic boundary conditionsAbout kernel of inverse operator L' to third-order derivative's Ly = −y+q(x)y operatorArticle