一类含一阶导数的四阶边值问题正解的全局结构  

Global structure of the positive solution for a class of fourth-order boundary value problems with first derivative

作　　者：张亚莉 ZHANG Ya-li(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2020年第8期102-110,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11671322)。

摘　　要：考察了一类含一阶导数的四阶边值问题{u(4)(t)=rf(t,u(t),u'(t)),t∈(0,1),u(0)=u'(0)=u″(1)=u■(1)=0}正解的全局结构,其中r是正参数,f:[0,1]×[0,∞)×[0,∞)→[0,∞)连续,且f(t,0,0)=0。当参数r在一定范围内变化时,运用Rabinowitz全局分歧定理获得了该问题正解的全局结构,所得结果推广并改进了已有的相关结果。This paper considers the global structure of positive solutions for a fourth-order boundary value problem with first derivative{u(4)(t)=rf(t,u(t),u'(t)),t∈(0,1),u(0)=u'(0)=u″(1)=u■(1)=0},where r is a positive parameter,f:[0,1]×[0,∞)×[0,∞)→[0,∞)is continuous,and f(t,0,0)=0.When the parameter r changes in a certain range,the global structure of positive solutions of the problem are obtained by using the Rabinowitz global bifurcation theorems.The conclusions in this paper generalize and improve the related results.

关 键 词：四阶 正解 主特征值 分歧定理 

分 类 号：O175.8[理学—数学] O175.14[理学—基础数学]