Continuity of periodic solutions of the Landesman–Lazer equation in external forces

Abstract

In this paper we study the continuity of periodic solutions of the Landesman–Lazer equations in coefficient functions. It will be proved that these periodic solutions are not only continuous in coefficient functions with respect to the usual Lp topologies, but also with respect to the weak topologies of the Lp spaces. The continuity results of this paper are the basis to study some quantities defined from solutions in a quantitative way.