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Dynamical behaviors for generalized pendulum type equations with p-Laplacian 认领

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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 ∫0^1 p(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.
出处 《中国数学前沿:英文版》 SCIE CSCD 2020年第5期959-984,共26页 Frontiers of Mathematics in China
基金 supported in part by the National Natural ScienceFoundation of China(Grant No.11971059) the Postdoctoral Applied Research ProjectFunding of Qingdao.
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