Boundedness of solutions for the reversible system with low regularity in time

2018/02/23 by Li, Jing
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.08459

Abstract

In the present paper, it is proved that all solutions are bounded for the reversible system x+∑_i=0^lb_i(t)x²ⁱ⁺¹x+x²ⁿ⁺¹+∑_i=0^n-1a_i(t)x²ⁱ⁺¹=0, 0≤ l≤ [(n)/(2)]-1,t∈\mathbbT¹=ℝ/ℤ, where a_i(t)∈ C¹(\mathbbT¹) ([(n-1)/(2)]+1≤ i≤ n-1), a_j(t)∈ L¹(\mathbbT¹) (0≤ j≤ [(n-1)/(2)]) and b_k(t)∈ C¹(\mathbbT¹) (0≤ k≤ l).

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