带积分条件的四阶微分算子的谱特性

IF 0.8 Q2 MATHEMATICS Lobachevskii Journal of Mathematics Pub Date : 2024-08-22 DOI:10.1134/s1995080224601188

R. D. Karamyan, A. L. Skubachevskii

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引用次数: 0

摘要

摘要我们考虑了一个普通四阶微分方程，该方程有一个谱参数，积分条件包含一个未知函数导数的线性组合。根据等效规范，我们得到了在谱参数值足够大的情况下该问题解的先验估计值。利用这些估计值，证明了问题的离散性、谱的扇形结构和弗雷德霍姆可解性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Spectral Properties of the Fourth Order Differential Operator with Integral Conditions

Abstract

We consider an ordinary fourth-order differential equation with a spectral parameter and integral conditions containing a linear combination of derivatives of an unknown function. In terms of equivalent norms, a priori estimates for solutions of this problem are obtained for sufficiently large values of the spectral parameter. Using these estimates, the discreteness, the sectorial structure of spectrum, and the Fredholm solvability of problem are proven.

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来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

期刊介绍： Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.

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