Spectral problem for the sixth order nonclassical differential equations

Alexander Ivanovich Kozhanov, Bakytbek Danebekovich Koshanov, Zh.B. Sultangaziyeva, A.N. Yemir Kady oglu, Gulzhazira D. Smatova

2020

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DOI 10.31489/2020m1/79-86

Data confidence 70 medium

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Abstract

Spectral problem for the sixth order nonclassical differential equationsIn this article we investigate the correctness of boundary value problems for a sixth order quasi-hyperbolic equation in the Sobolev spaceFor the given operator L two spectral problems are introduced and uniqueness of these problems is established.The eigenvalues and eigenfunctions of the first spectral problem are calculated for the sixth order quasi-hyperbolic equation.In this work we show that the equation Lu = 0 for λ < 0 under uniform conditions has a countable set of nontrivial solutions.Usually, this does not happen when the operator L is an ordinary hyperbolic operator.