非自治二阶次线性微分方程的同宿轨

努尔别克·艾孜玛洪; 安天庆

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非自治二阶次线性微分方程的同宿轨

更新时间：2026-01-21

- 非自治二阶次线性微分方程的同宿轨
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 29, Issue 1, Pages: 58-65(2012)
- 作者机构：
  
  1. 河海大学理学院
  2. 新疆农业大学数理学院
- 作者简介：
- 基金信息：
- DOI：
  CLC： O175
- Published：2012
- 稿件说明：
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[1]努尔别克·艾孜玛洪,安天庆.非自治二阶次线性微分方程的同宿轨[J].新疆大学学报(自然科学版),2012,29(01):58-65.

努尔别克·艾孜玛洪, 安天庆. 非自治二阶次线性微分方程的同宿轨[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2012, 29(1): 58-65.
[1]努尔别克·艾孜玛洪,安天庆.非自治二阶次线性微分方程的同宿轨[J].新疆大学学报(自然科学版),2012,29(01):58-65. DOI：

努尔别克·艾孜玛洪, 安天庆. 非自治二阶次线性微分方程的同宿轨[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2012, 29(1): 58-65. DOI：

摘要

通过临界点理论中的经典最小化原则

讨论二阶非自治微分方程ü+Au+L(t)u+Fu(t

u)=0在非线性项F为次线性条件下同宿轨的存在性

回答了同宿轨非平凡性和唯一性等问题.这里的次线性条件为:存在函数f

g∈L1(R

R+)和常数1

Abstract

This paper showed the homoclinic solutions for nonautonomous second order systems ü+Au+L(t)u+Fu(t

u) = 0.Assuming that F is sublinear

that is

there exist functions f

g ∈ L(R

R+) such that |Fu(t

u)| ≤ f(t)|u|γ 1+ g(t)

where 1 < γ ≤ 2 and F(t

0) ∈ L(R

we establish some existence results to guarantee that system has at least one nontrivial and unique homoclinic solution by using a standard minimizing argument.

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Keywords

references

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