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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (6): 88-95.doi: 10.6040/j.issn.1671-9352.0.2018.344

• • 上一篇    

一类非线性二阶系统周期边值问题正解的存在性

马满堂   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2019-06-05
  • 作者简介:马满堂(1995— ), 男, 硕士研究生, 研究方向为常微分方程边值问题. E-mail:mantangma@163.com
  • 基金资助:
    国家自然科学基金资助项目(11671322)

Existence of positive solutions for a class of periodic boundary value problems of nonlinear second-order systems

MA Man-tang   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2019-06-05

摘要: 考察了非线性二阶系统周期边值问题{u″+A(t)u=ΛG(t)F(u), 01,…,un)T, A(t)=diag[a1(t),…,an(t)], ai(t)可变号(i=1,…,n), G(t)=diag[g1(t),…,gn(t)], F(u)=(f1(u),…, fn(u))T, Λ=diag1,…,λn), λi为正参数(i=1,…,n)。在非线性项F满足超线性,次线性和渐近线性的条件下,本文运用锥拉伸与压缩不动点定理获 得了该问题正解的存在性,所得结论推广和改进了已有的相关结果。

关键词: 正解, 系统, 锥, 存在性

Abstract: We consider the existence of positive solutions for the periodic boundary value problems of nonlinear second-order systems{u″+A(t)u=ΛG(t)F(u), 01,…,un)T, A(t)=diag[a1(t),…,an(t)], ai(t)can change the sign in [0,1] (i=1,…,n), G(t)=diag[g1(t),…,gn(t)], F(u)=(f1(u),…, fn(u))T, Λ=diag1,…,λn), λi is a positive parameter(i=1,…,n). Under the assumption that the nonlinear term F satisfies superlinear, sublinear and asymptotic growth condition, the existence of positive solutions of the problem are obtained by using the fixed-point theorem of cone expansion-compression. The conclusions in this paper generalize and improve the related results.

Key words: positive solutions, systems, cone, existence

中图分类号: 

  • O175.8
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