一类非线性二阶系统周期边值问题正解的存在性

doi:10.6040/j.issn.1671-9352.0.2018.344

摘要/Abstract

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,…,u_n)T, A(t)=diag［a₁(t),…,a_n(t)］, a_i(t)可变号(i=1,…,n), G(t)=diag［g₁(t),…,g_n(t)］, F(u)=(f₁(u),…, f_n(u))T, Λ=diag(λ₁,…,λ_n), λ_i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,…,u_n)T, A(t)=diag［a₁(t),…,a_n(t)］, a_i(t)can change the sign in ［0,1］ (i=1,…,n), G(t)=diag［g₁(t),…,g_n(t)］, F(u)=(f₁(u),…, f_n(u))T, Λ=diag(λ₁,…,λ_n), λ_i 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

马满堂. 一类非线性二阶系统周期边值问题正解的存在性[J]. 《山东大学学报(理学版)》, 2019, 54(6): 88-95.

MA Man-tang. Existence of positive solutions for a class of periodic boundary value problems of nonlinear second-order systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 88-95.

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