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Spectral and oscillatory properties of a linear pencil of fourth-order differential operators |
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| Authors: | J. Ben Amara A. A. Shkalikov A. A. Vladimirov |
| Affiliation: | 1. University of 7th November at Carthage, Carthage, Tunisia 2. Moscow State University, Moscow, Russia 3. Dorodnicyn Computing Center, Russian Academy of Sciences, Moscow, Russia |
| Abstract: | The paper deals with the spectral and oscillatory properties of a linear operator pencilA ? λB, where the coefficient A corresponds to the differential expression (py″)″ and the coefficient B corresponds to the differential expression ?y″ + cry. In particular, it is shown that all negative eigenvalues of the pencil are simple and, under some additional conditions, the number of zeros of the corresponding eigenfunctions is related to the serial number of the corresponding eigenvalue. |
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