A Variational Method For The Existence of Bounded Solutions of a Sublinear Forced Oscillator |
| |
| Authors: | Ortega Rafael; Verzini Gianmaria |
| |
| Institution: | Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada 180071 Granada, Spain; E-mail: rortega{at}ugr.es
Dipartimento di Matematica, Politecnico di Milano Piazza L. da Vinci 32, 20133 Milano, Italy; E-mail: gianmaria.verzini{at}polimi.it |
| |
| Abstract: | We prove that, for every bounded and measurable forcing p(t),the differential equation  has bounded solutions with arbitrarily large amplitude. In generalit is not possible to say that all solutions are bounded, asshown by an example due to Littlewood. The proof is based on a variational method which can be seenas a dual version of Nehari's method for boundary value problemson compact intervals. 2000 Mathematics Subject Classification34C11, 34B14, 49J35. |
| |
| Keywords: | bounded solution minimax Nehari's method |
| 本文献已被 Oxford 等数据库收录！ |
|
