Leonid V. Kritskov, Abdizhahan M. Sarsenbi
We consider the differential equation
with the nonlocal boundary conditions , where . We prove that if is irrational then the system of its eigenfunctions is complete and minimal in for any , but does not constitute a basis. In the case of a rational value of r we specify the way of choosing the associated functions which provides the system of all root functions of the problem forms a basis in .
Submitted October 17, 2015. Published November 4, 2015.
Math Subject Classifications: 34K08, 34L10, 46B15.
Key Words: ODE with involution; nonlocal boundary-value problem; basicity of root functions.
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| Leonid V. Kritskov |
Lomonosov Moscow State University
Faculty of Computational Mathematics and Cybernetics
119899 Moscow, Russia
| Abdizhahan M. Sarsenbi |
Auezov South-Kazakhstan State University
Department of Mathematical Methods and Modeling
160012 Shymkent Kazakhstan
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