带Stieltjes积分边值条件奇异简支梁方程正解的全局分歧  

Global Bifurcation of Positive Solutions for Singular Beam Equation with Simply Supported Involving Stieltjes Integral Conditions

作　　者：沈文国[1] 

机构地区：[1]兰州工业学院基础学科部,甘肃兰州730050

出　　处：《应用数学》2016年第4期881-889,共9页Mathematica Applicata

基　　金：国家自然科学基金(11561038);甘肃省自然科学基金(145RJZA087)

摘　　要：本文研究带Riemann-Stieltjes积分边值条件两端简单支撑梁的奇异四阶边值问题正解的全局分歧结构.首先,利用相关文献,获得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,建立此类问题正解的全局结构,进而获得正解的存在性,并且将此类方法推广到不同边值条件时的情形.In this paper, we establish global bifurcation structure of positive solutions for a class of fourth-order problems with the deformations of an elastic beam in an equilibrium state, whose both ends are simple supported. Firstly, by relevant literature, we obtain that the Green ruction and its property for the problem. Meanwhile, we can obtain that the above problem is equivalent to the completely continuous operator equation. Secondly, 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. This kind of method can be extended to more general situation.

关 键 词：奇异四阶积分边值问题 全局分歧 正解 

分 类 号：O175.8[理学—数学]