﻿ 四阶不定微分算子非实特征值的估计 Estimates on the Non-Real Eigenvalues of Fourth Order Indefinite Differential Operators

Pure Mathematics
Vol.07 No.03(2017), Article ID:20483,8 pages
10.12677/PM.2017.73017

Estimates on the Non-Real Eigenvalues of Fourth Order Indefinite Differential Operators

Fan Hu, Jiong Sun, Kun Li, Xiaoling Hao

School of Mathematical Sciences, Inner Mongolia University, Hohhot Inner Mongolia

Received: Apr. 21st, 2017; accepted: May 6th, 2017; published: May 10th, 2017

ABSTRACT

The present paper gives an estimate on the non-real eigenvalues for a class of fourth order differential operators. Using operator theory and classical analysis, we study the eigenvalue problem for indefinite differential operators produced by the signs of weight function, and discuss the cases of many turning points and a turning point for the weight function respectively, then we get the estimate on the real and imaginary parts of the non-real eigenvalues.

Keywords:Fourth Order Differential Operators, Non-Real Eigenvalue, Indefinite Weight Function

1. 引言

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2. 正文

，定义。因为a.e.

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3. 结论

3.1. 权函数具有多个拐点时非实特征值的估计

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3.2. 权函数只有一个拐点时非实特征值的估计

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Estimates on the Non-Real Eigenvalues of Fourth Order Indefinite Differential Operators[J]. 理论数学, 2017, 07(03): 141-148. http://dx.doi.org/10.12677/PM.2017.73017

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