On the set of periods of periodic solutions of a model quasilinear differential equation

Abstract

Quasilinear differential equations of the form Lu = F (u), where L is a linear differential operator and F (u) is a nonlinear part satisfying the Lipschitz condition, can be studied most easily for the case in which the operator L has a bounded inverse in the corresponding spaces. Then the original equation can be reduced to an equation of the form u = L−1F (u), to which one can apply the contraction mapping method. However, it often turns out that the inverse of L exists but is unbounded.