Optimal lower bound for the first eigenvalue of the fourth order equation

Gang Meng School of Mathematical Sciences, University of Chinese Academy of Sciences Ping Yan Department of Mathematical Sciences, Tsinghua University

Classical Analysis and ODEs mathscidoc:1611.05001

J. Differential Equations, 261, 3149–3168, 2016
In this paper we will find optimal lower bound for the first eigenvalue of the fourth order equation with integrable potentials when the L1norm of potentials is known. We establish the minimization character-ization for the first eigenvalue of the measure differential equation, which plays an important role in the extremal problem of ordinary differential equation. The conclusion of this paper will illustrate a new and very interesting phenomenon that the minimizing measures will no longer be located at the center of the interval when the norm is large enough.
eigenvalue, fourth order equation, lower bound
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@inproceedings{gang2016optimal,
  title={Optimal lower bound for the first eigenvalue of the fourth order equation},
  author={Gang Meng, and Ping Yan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161124075443706356634},
  booktitle={J. Differential Equations},
  volume={261},
  pages={3149–3168},
  year={2016},
}
Gang Meng, and Ping Yan. Optimal lower bound for the first eigenvalue of the fourth order equation. 2016. Vol. 261. In J. Differential Equations. pp.3149–3168. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161124075443706356634.
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