Hongjie Guo, Jiangang Qi
Abstract:
For the n-th eigenvalue of a Sturm-Liouville eigenvalue problem with
separated boundary conditions, we express the infimum of the
norm of potentials, in terms of a parameter
and the boundary
conditions. Also we indicate where the infimum can be attained.
As an application, we obtain the extremum of the n-th eigenvalue of a
problem for potentials on a sphere in
.
Submitted January 7, 2017. Published April 11, 2017.
Math Subject Classifications: 34B20, 34L99, 34L05.
Key Words: Sturm-Liouville problem; eigenvalue; inverse problem;
Lyapunov-type inequality; extremal problem.
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Hongjie Guo Department of Mathematics Shandong University at Weihai Weihai 264209, China email: ghj790629@163.com | |
Jiangang Qi Department of Mathematics Shandong University at Weihai Weihai 264209, China email: qijiangang@sdu.edu.cn |
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