A variational method for the existence of bounded solutions of a sublinear forced oscillator
Rafael Ortega, Gianmaria Verzini · Proceedings of the London Mathematical Society · 2004
We prove that, for every bounded and measurable forcing p(t), the differential equation u ¨ + u 1 / 3 = p ( t ) has bounded solutions with arbitrarily large amplitude. In general it is not possible to say that all solutions are bounded, as shown by an example due to Littlewood. The proof is based on a variational method which can be seen as a dual version of Nehari's method for boundary value problems on compact intervals. 2000 Mathematics Subject Classification 34C11, 34B14, 49J35.