Nonlocal multipoint problem for an ordinary differential equations of even order involution
Journal Title: Математичні Студії - Year 2018, Vol 49, Issue 1
Abstract
We study a nonlocal multipoint problem for an ordinary differential equation of even order with coefficients containing an involution operator. The spectral properties of a self-adjoint operator with boundary conditions generalizing the conditions of antiperiodicity are investigated. For a differential equation of even order, we consider a problem with multipoint conditions that are perturbations of self-adjoint boundary conditions. We study cases when multipoint conditions include boundary conditions that are regular, but not strongly regular according to Birkhoff, or irregular. The eigenvalues and elements of the system of the root functions of the operator of the problem are determined. It is proved that the system is complete and contains an infinite number of associated functions. Sufficient conditions are obtained for which this system is a Riesz basis. Similar results are obtained for the operator generated by the multipoint problem for an ordinary differential equation of even order with coefficients containing the involution operator.
Authors and Affiliations
Ya. Baranetskij, P. Kalenyuk, L. Kolyasa, M. Kopach
Keywords
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- EP ID EP355321
- DOI 10.15330/ms.49.1.80-94
- Views 45
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