吉林大学学报（理学版）2025，Vol.63Issue(3)：733-739,7.DOI:10.13413/j.cnki.jdxblxb.2024314
一类四阶非齐次边值问题正解的存在性与多解性
Existence and Multiplicity of Positive Solutions for a Class of Fourth-Order Nonhomogeneous Boundary Value Problems
摘要
Abstract
By using Leray-Schauder degree theory and method of upper and lower solutions,the author study the existence and multiplicity of positive solutions for the elastic beam equation with nonhomogeneous boundary conditions{u("")(t)=f(t,u(t)),t∈(0,1),{u(0)=0,u'(0)=b,u"(1)=u(''')(1)=0,where b＞0,f ∈ C([0,1]× R+,R+),and f(t,s)is a monotone increasing function with respect to s.When the nonlinear term f satisfies suitable conditions,the author prove that there is a positive number b*,such that there are at least two positive solutions to the problem when 0＜b＜b*,there is exactly one positive solution to the problem when b=b*,there is no positive solution to the problem when b＞b*.关键词
正解/非齐次/Leray-Schauder度/上下解方法Key words
positive solution/nonhomogeneous/Leray-Schauder degree/method of upper and lower solutions分类
数理科学引用本文复制引用
程虎文..一类四阶非齐次边值问题正解的存在性与多解性[J].吉林大学学报（理学版）,2025,63(3):733-739,7.基金项目
国家自然科学基金(批准号:12061064). （批准号:12061064）
