Mather sets for sublinear Duffing equations
type: Item
instance of: scholarly article
title: Mather sets for sublinear Duffing equations
zbMATH Open document ID: 0823.34049
published in: Chinese Annals of Mathematics. Series B
publication date: 1995-02-09T00:00:00Z
review text: The paper deals with the Duffing equation \(x'' + g(x) = p(t)\) with sublinear growth conditions, where \(p(t)\) is periodic and \(g\) satisfies some regularity conditions. The author studies the existence of so-called Mather sets, which are sets of generalized quasiperiodic and unlinked periodic solutions. The main theorem gives conditions under which there exists a \(W > 0\) such that for any \(0 < w < W\), the equation possesses a solution \(z(w)\) of Mather type with rotation number \(w\). It follows that (i) if \(w\) is a rational number \(p/q\), there are \(q\) periodic solutions \(\{z(w)\}\) of period \(q\); (ii) if \(w\) is an irrational number then the solution \(z(w)\) is either a usual quasiperiodic solution or a generalized one exhibiting a Denjoy's minimal set \(M(w)\).
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 720561
zbMATH Keywords: Duffing equation
zbMATH Keywords: Mather sets
zbMATH Keywords: periodic solutions
zbMATH Keywords: quasiperiodic solution
zbMATH Keywords: Denjoy's minimal set
author: Dingbian Qian
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 720561