Dynamical behaviors for generalized pendulum type equations with p-Laplacian

被引：0
作者：
Yanmin Niu
Xiong Li
机构：
[1] Ocean University of China,School of Mathematical Sciences
[2] Beijing Normal University,Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences
来源：
Frontiers of Mathematics in China | 2020年 / 15卷
关键词：
-Laplacian; invariant tori; quasi-periodic solutions; boundedness; complex dynamics; 37C55; 37C75; 37B10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider a pendulum type equation with p-Laplacian (ϕp (x′))′ + G′x(t, x) = p(t), where ϕp(u) = ∣u∣p−2u, p > 1, G(t, x) and p(t) are 1-periodic about every variable. The solutions of this equation present two interesting behaviors. On the one hand, by applying Moser’s twist theorem, we find infinitely many invariant tori whenever ∫01p(t)dt = 0, which yields the boundedness of all solutions and the existence of quasi-periodic solutions starting at t = 0 on the invariant tori. On the other hand, if p(t) = 0 and G′x (t, x) has some specific forms, we find a full symbolic dynamical system made by solutions which oscillate between any two different trivial solutions of the equation. Such chaotic solutions stay close to the trivial solutions in some fixed intervals, according to any prescribed coin-tossing sequence.
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页码：959 / 984
页数：25
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