Browsing by Author "Uxikbayev K.B."

Now showing 1 - 1 of 1
  • Thumbnail Image
    ItemUnknown
    Solution of differential equations with vertical asymptotes
    (Suleyman Demirel University, 2011) Uxikbayev K.B.
    This 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.