Triple positive solution to the one-dimensional $p$-Laplacian equation

Abstract

We obtain sufficient conditions for the existence of at least three positive solutions to the second-order nonlinear delay differential equation with one-dimensional $p$-Laplacian

where $\Phi p(s)$ is the $p$-Laplacian operator, i.e., ${\Phi }_p(s)=|s{|}^{p-2}s$, $p>1$, $({\Phi }_p{)}^{-1}={\Phi }_q$, $\frac{1}{p}+\frac{1}{q}=1$. The arguments are based upon a new fixed point theorem in a cone introduced by Avery and Peterson.