Periodic Problem Involving Quasilinear Differential Operator and Weak Singularity

Abstract

Abstract We study the singular periodic boundary value problem of the form (|u′|p−2 u′)′ = f(t, u), u(0) = u(T), u′(0) = u′(T), where 1 < p < ∞ and f ∈ Car([0, T] × (0,∞)) can have a repulsive space singularity at x = 0. Contrary to previous results by Mawhin and Jebelean, Liu Bing and Rachůnková and Tvrdý, we need not assume any strong force conditions. Our main existence results rely on a new antimaximum principle for periodic quasilinear periodic problem, which has an independent meaning.