奇异高阶积分边值问题正解的全局结构

摘要

本文研究了带Riemann-Stieltjes积分边值条件的奇异高阶积分边值问题正解的全局分歧结构.利用相关文献,获得了此类问题的格林函数并推证其满足的性质,同时可获得此类问题等价于一个全连续算子方程;其次,在满足所给的条件时,利用Krein-Rutmann定理建立了此类问题对应的线性问题存在简单的主特征值;最后,当非线性项在零和无穷远处满足非渐进线性增长条件、参数满足不同范围的值时,利用Dancer全局分歧定理、Zeidler全局分歧定理和序列集取极限的方法,建立了此类问题正解的全局结构,进而获得了正解的存在性,推广了文献[8]中的主要结果.%In this paper, we establish global bifurcation structure of positive solutions for a class of singular higher-order boundary value problems. First, according to the relevant literature, we obtain that the Green fuction and its property for the above problem. Meanwhile, we can obtain that the above problem is equivalent to the completely continuous operator equation. Second, we have that the above linear problem exists simple principal eigenvalue by the Krein-Rutman theorem. Finally, we establish the global bifurcation structure of positive solutions with non-asymptotic nonlinearity at or by Dancer and Zeidler global bifurcation theorems and the approximation of connected components which extends and improves the corresponding results of Shen [8].