Extremum estimates of the $ L^1 $-norm of weights for eigenvalue problems of vibrating string equations based on critical equations

Jiangang Qi; Bing Xie

doi:10.3934/dcdsb.2020243

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2021, Volume 26, Issue 7: 3505-3516. Doi: 10.3934/dcdsb.2020243

This issue Previous Article Moran process and Wright-Fisher process favor low variability Next Article Regular dynamics for stochastic Fitzhugh-Nagumo systems with additive noise on thin domains

Extremum estimates of the $ L^1 $-norm of weights for eigenvalue problems of vibrating string equations based on critical equations

Jiangang Qi and
Bing Xie^,

School of Mathematics and Statistics, Shandong University, Weihai 264209, China

^* Corresponding author: Bing Xie
^* Corresponding author: Bing Xie

Received: October 31, 2019

Early access: August 2020

Published: July 2021

The first author is supported by the NSF of China grants 11771253, 11971262 and 61977043. The second author is supported by NSF of the Shandong Province grants ZR2019MA038, ZR2019MA050 and ZR2017MA049

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Abstract

The present paper is concerned with the extremal problem of the $ L^1 $-norm of the weights for non-left-definite eigenvalue problems of vibrating string equations with separated boundary conditions. Applying the critical equations of the weights, the infimum is obtained in terms of the given eigenvalue and the parameter in boundary conditions.

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Mathematics Subject Classification: Primary:34B24;Secondary:34L15.

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