Open AccessPeriodic solutions of some classes of continuous second-order differential equations
Author(s) -
Jaume Llibre,
Abdenacer Makhlouf
Publication year - 2017
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2017022
Subject(s) - lipschitz continuity , order (exchange) , differential equation , continuous function (set theory) , function (biology) , mathematics , mathematical analysis , combinatorics , mathematical physics , physics , finance , evolutionary biology , economics , biology
We study the periodic solutions of the second--order differential equations of the form x x^n = f(t), or x $^ n = f(t) are only continuous in t and locally--Lipschitz in x. ^ n = f(t), where n=4,5, f(t) is a continuous T--periodic function such that _0^T f(t)dt 0, and is a positive small parameter. Note that the differential equations x x^n = f(t) are only continuous in t and smooth in x, and that the differential equations