Distribution of the Prufer angle in p-Laplacian eigenvalue problems

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 $(0,\pi_p)$.

Keywords

• p-Laplacian eigenvalue problem
• Prufer angle
• equidistribution
• uniform distribution