Unbounded Motions in Asymmetric Oscillators Depending on Derivatives

WANG Li-xia, MA Shi-wang, WANG Xiao-ming

doi:10.13371/j.cnki.chin.q.j.m.2016.02.010

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 2: 189 - 200

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.02.010

Unbounded Motions in Asymmetric Oscillators Depending on Derivatives

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1. School of Science,Tianjin Chengjian University2. School of Mathematical Sciences and LPMC,Nankai University3. School of Mathematics and Computer Science,Shangrao Normal University

WANG Li-xia(1982-), female, native of Shijiazhuang, Hebei, a lecturer of Tianjin Chengjian University, Ph.D., engages in dynamical system and di®erential equations; MA Shi-wang(1968-), male, native of Eerduosi, Neimenggu, a professor of Nankai University, Ph.D., engages in dynamical system and di®erential equations; WANG Xiao-ming(corresponding author)(1978-), male, native of Yushan, Jiangxi, an associate professor of Shangrao Normal University, engages in dynamical system and di®erential equations.

Received date: 2014-10-15

Online published: 2020-11-06

Supported by

Supported by the Tianyuan Special Foundation(11526148)； Supported by the National Natural Science Foundation of China(11571187,11461056)；

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Abstract

In this paper, we consider the unboundedness of solutions for the asymmetric equation x^’’+ax⁺-bx^-+（x）ψ（x^’）+f（x）+g（x’）=p（t）,where x⁺= max{x, 0}, x^-= max{-x, 0}, a and b are two different positive constants,f（x） is locally Lipschitz continuous and bounded, （x）, ψ（x）, g（x） and p（t） are continuous functions, p（t） is a 2π-periodic function. We discuss the existence of unbounded solutions under two classes of conditions: the resonance case 1/a^1/2+1/b^1/2∈Q and the nonresonance case 1/a^1/2+1/b^1/2∈Q

Key words： unboundedness; resonance; nonresonance

Cite this article

WANG Li-xia, MA Shi-wang, WANG Xiao-ming . Unbounded Motions in Asymmetric Oscillators Depending on Derivatives[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(2) : 189 -200 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.02.010

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