Electron. J. Diff. Equ., Vol. 2014 (2014), No. 255, pp. 1-8.

Distribution of the Prufer angle in $p$-Laplacian eigenvalue problems

Yan-Hsiou Cheng, Chun-Kong Law, Yu-Chen Luo

Abstract:
The Prufer angle is an effective tool for studying Sturm-Liouville problems and p-Laplacian eigenvalue problems. In this article, we show that for the p-Laplacian eigenvalue problem, when x is irrational in (0,1), a sequence of modified Prufer angles (after modulo $\pi_p$) is equidistributed in $(0,\pi_p)$. As a function of x, $\psi_n$ is also asymptotic to the uniform distribution on (0,\pi_p).

Submitted November 11, 2014. Published December 4, 2014.
Math Subject Classifications: 34B24, 37A30
Key Words: p-Laplacian eigenvalue problem; Prufer angle; equidistribution; uniform distribution.

Show me the PDF file (212 KB), TEX file, and other files for this article.

Yan-Hsiou Cheng
Department of Mathematics and Information Education
National Taipei University of Education
Taipei 106, Taiwan
email: yhcheng@tea.ntue.edu.tw
Chun-Kong Law
Department of Applied Mathematics
National Sun Yat-sen University
Kaohsiung 80424, Taiwan
email: law@math.nsysu.edu.tw
Yu-Chen Luo
Department of Applied Mathematics
National Sun Yat-sen University
Kaohsiung 80424, Taiwan
email: leoredro@gmail.com

Return to the EJDE web page