Basis properties of eigenfunctions of the 𝑝-Laplacian

Abstract

For p ⩾ 12 11 p\geqslant \frac {12}{11} , the eigenfunctions of the non-linear eigenvalue problem for the p p -Laplacian on the interval ( 0 , 1 ) (0,1) are shown to form a Riesz basis of L 2 ( 0 , 1 ) L_2(0,1) and a Schauder basis of L q ( 0 , 1 ) L_q(0,1) whenever 1 > q > ∞ 1>q>\infty .