## Differential and Integral Equations

### Remarks on eigenfunction expansions for the p-Laplacian

Wei-Chuan Wang

#### Abstract

The one-dimensional $p$-Laplacian eigenvalue problem \begin{equation*} \begin{cases} -(|y'|^{p-2}y')'=(p-1)(\lambda -q(x))|y|^{p-2}y,\\ y(0)=y(1)=0, \end{cases} \end{equation*} is considered in this paper. We derive its normalized eigenfunction expansion by using a Prüfer-type substitution. Employing some theories in Banach spaces, we discuss the basis property related to these eigenfunctions as an application.

#### Article information

Source
Differential Integral Equations, Volume 32, Number 9/10 (2019), 583-594.

Dates
First available in Project Euclid: 13 August 2019

https://projecteuclid.org/euclid.die/1565661624

Mathematical Reviews number (MathSciNet)
MR3992038

#### Citation

Wang, Wei-Chuan. Remarks on eigenfunction expansions for the p-Laplacian. Differential Integral Equations 32 (2019), no. 9/10, 583--594. https://projecteuclid.org/euclid.die/1565661624