A Landesman–Lazer Type Theorem for Periodic Solutions of the Resonant Asymmetric p–Laplacian Equation

Abstract

In this paper, we give a Landesman–Lazer type theorem for periodic solutions of the asymmetric 1–dimensional p-Laplacian equation

$$ - {\left( {{\left| {{x}'} \right|}^{{p - 2}} {x}'} \right)}^{\prime } = \lambda {\left| x \right|}^{{p - 2}} x_{ + } + \mu {\left| x \right|}^{{p - 2}} x_{ - } + f{\left( {t,x} \right)} $$

with periodic boundary value.