吉林大学学报（理学版）2025，Vol.63Issue(3)：709-715,7.DOI:10.13413/j.cnki.jdxblxb.2024287
一类完全四阶非线性常微分方程边值问题正解的存在性
Existence of Positive Solutions to Boundary Value Problems for a Class of Fully Fourth-Order Nonlinear Ordinary Differential Equations
摘要
Abstract
By using Leray-Schauder fixed point theorem,we study a class of fully fourth-order nonlinear ordinary differential equations{u(4)(t)=f(t,u(t),u'(t),u"(t),u(''')(t)),t∈[0,1],{u(0)=u'(0)=u'(1)=u(''')(1)=0,where f∈C([0,1]× R4,R+).The existence and uniqueness of the positive solutions are proven under the condition that the nonlinear term f grows at most linearly.Under the condition that f satisfies the superlinear growth,the existence of positive solutions are obtained by introducing a Nagumo-type condition to limit that f(t,x0,x1,x2,x3)is quadratical growth on x3 at most.关键词
完全四阶非线性边值问题/正解/存在性/唯一性/Leray-Schauder不动点定理/Nagumo型条件Key words
fully fourth-order nonlinear boundary value problem/positive solution/existence/uniqueness/Leray-Schauder fixed point theorem/Nagumo-type condition分类
数理科学引用本文复制引用
胡万民,韩晓玲..一类完全四阶非线性常微分方程边值问题正解的存在性[J].吉林大学学报（理学版）,2025,63(3):709-715,7.基金项目
国家自然科学基金(批准号:12161079). （批准号:12161079）
