Electron. J. Differential Equations, Vol. 2016 (2016), No. 283, pp. 1-12.

Structure and asymptotic expansion of eigenvalues of an integral-type nonlocal problem

Zhong-Cheng Zhou, Fang-Fang Liao

Abstract:
We study the structure of eigenvalues of second-order differential equations with nonlocal integral boundary conditions. Moreover, we consider the asymptotic expansion of the eigenvalues and the corresponding eigenfunctions, which shows that the eigenfunctions form a Riesz basis for $L^2([0,1],\mathbb{R})$.

Submitted June 24, 2016. Published October 24, 2016.
Math Subject Classifications: 34C25, 34D20.
Key Words: Eigenvalues; asymptotic expansion; nonlocal problem; Riesz basis.

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Zhong-Cheng Zhou
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: zhouzc@amss.ac.cn
Fang-Fang Liao
Department of Mathematics
Shanghai Normal University
Shanghai 200234, China
email: liaofangfang8178@sina.com

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