Nonlinear resonance in asymmetric oscillations

摘要

In this paper we study the periodic problem (ϕp(x′))′+αϕp(x+)−βϕp(x−)=f(x,t), where ϕp(u)=|u|p−2u, p>1, α−1/p+β−1/p=2n−1, n∈N. By computing the associated topological degree we prove existence of periodic solutions and stability of large amplitude oscillations for equations with a small damping term.