Spectral properties of the equation of a vibrating rod at both ends of which the masses are concentrated
| Autor: | Ziyatkhan S. Aliyev, Faiq M. Namazov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
Basis (linear algebra) Oscillation 010102 general mathematics Mathematical analysis 0211 other engineering and technologies 021107 urban & regional planning 02 engineering and technology Operator theory Eigenfunction Space (mathematics) 01 natural sciences Ordinary differential equation Boundary value problem 0101 mathematics Analysis Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Banach Journal of Mathematical Analysis. 14:585-606 |
| ISSN: | 1735-8787 2662-2033 |
| DOI: | 10.1007/s43037-019-00009-1 |
| Popis: | In this paper we consider a spectral problem for ordinary differential equation of fourth order with a spectral parameter in the boundary conditions. This problem arises when variables are separated in the dynamical boundary value problem describing bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the both ends of which are fixed elastically and on these ends the masses are concentrated. We investigate locations, multiplicities of eigenvalues, study the oscillation properties of eigenfunctions and establish sufficient conditions for the subsystems of root functions of this problem to form a basis in the space $$L_p,\,1< p < \infty $$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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