浙江大学学报（理学版）2025，Vol.52Issue(6)：699-705,7.DOI:10.3785/j.issn.1008-9497.2025.06.004
一类具有非线性导数项的弹性梁方程正解的存在性
Existence of positive solutions for a class of elastic beam equations with nonlinear derivative terms
摘要
Abstract
The existence of positive solutions are discussed for the fourth-order boundary value problems with nonlinear derivative terms u()4(x)=f(x,u(x),u'(x))on[0,1]where the boundary u'(0)=u‴(0)=u(1)=u'(1)=0,the condition models the deformations of the right side of a statically symmetrical elastic beam with fixed ends,where f:[0,1]×R+×R-→R+is continuous.Under the conditions that f(x,u,v)satisfies certain inequality,the existence results of positive solutions of this problem are obtained by applying the fixed point index theory in cones.The inequality conditions are related to the minimum positive real eigenvalue λ1 of the corresponding linear eigenvalue problem,and are an extension of the eigenvalue criteria for positive solutions of the normal ordinary differential boundary value problems.关键词
四阶边值问题/正解/特征值准则/锥/不动点指数Key words
fourth-order boundary value problems/positive solution/eigenvalue criteria/cone/fixed point index分类
数理科学引用本文复制引用
东智加,李永祥..一类具有非线性导数项的弹性梁方程正解的存在性[J].浙江大学学报（理学版）,2025,52(6):699-705,7.基金项目
国家自然科学基金资助项目(12061062). （12061062）
