依赖于导数项的非对称振子解的无界性

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

数学季刊 ›› 2016, Vol. 31 ›› Issue (2): 189-200.doi: 10.13371/j.cnki.chin.q.j.m.2016.02.010

依赖于导数项的非对称振子解的无界性

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

收稿日期:2014-10-15 出版日期:2016-06-30 发布日期:2020-11-06
作者简介: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.
基金资助:
Supported by the Tianyuan Special Foundation(11526148)； Supported by the National Natural Science Foundation of China(11571187,11461056)；

Unbounded Motions in Asymmetric Oscillators Depending on Derivatives

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

Received:2014-10-15 Online:2016-06-30 Published:2020-11-06
About author: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.
Supported by:
Supported by the Tianyuan Special Foundation(11526148)； Supported by the National Natural Science Foundation of China(11571187,11461056)；

摘要/Abstract

摘要： 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

关键词: unboundedness, resonance, nonresonance

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

中图分类号:

O175

王丽霞, 马世旺, 汪小明. 依赖于导数项的非对称振子解的无界性[J]. 数学季刊, 2016, 31(2): 189-200.

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.

依赖于导数项的非对称振子解的无界性

Unbounded Motions in Asymmetric Oscillators Depending on Derivatives

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