Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 139, pp. 111.
Eigenvalue problems with pLaplacian operators
YanHsiou Cheng
Abstract:
In this article, we study eigenvalue problems with the pLaplacian operator:
where p>1 and
.
We show that if
and q is singlewell with transition
point
, then the second Neumann eigenvalue is greater
than or equal to the first Dirichlet eigenvalue; the equality holds
if and only if q is constant.
The same result also holds for pLaplacian problem with
singlebarrier
and
. Applying these results,
we extend and improve a result by [24]
by using finitely many eigenvalues and by generalizing the string
equation to pLaplacian problem. Moreover, our results also extend
a result of Huang [14] on the estimate of the first instability
interval for Hill equation to singlewell function q.
Submitted November 7, 2013. Published June 16, 2014.
Math Subject Classifications: 34A55, 34L15.
Key Words: pLaplacian; inverse spectral problem; instability interval.
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YanHsiou Cheng
Department of Mathematics and Information Education
National Taipei University of Education
Taipei City 106, Taiwan
email: yhcheng@tea.ntue.edu.tw

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