一类带参数四阶边值问题正解的存在性  

Existence of positive solutions for a class of fourth-order boundary value problems with parameter

作　　者：杨丽娟 YANG Li-juan(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）》2021年第9期35-41,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11671322)。

摘　　要：研究了带参数四阶常微分方程(ordinary differential equation,ODE)边值问题{u^(′′′′)(t)+au^(′′′)+bu(^(′′))+cu′(t)+du(t)=rf(t,u(t),u^(′′)(t)),0<t<1,u(0)=u(1)=u^(′′)(0)=u^(′′)(1)=0,这里r是一个正参数,a、b、c、d为常系数,非线性项f:[0,1]×[0,∞)×(-∞,0]→[0,∞)为连续函数。当r在一定取值范围内,通过运用全局分歧理论,证明了该问题正解的存在性。This article studies the boundary value problems of fourth-order ordinary differential equations with parameter {u^(^(^(′′)′)′)(t)+au^(^(′′)′)+bu(^(′′))+cu′(t)+du(t)=rf(t,u(t),u^(′′)(t)),0<t<1,u(0)=u(1)=u^(′′)(0)=u^(′′)(1)=0, where r is a positive parameter,a,b,c,d are constant coefficients,and the nonlinearity f:[0,1]×[0,∞)×(-∞,0]→[0,∞)is a continuous function.When r is in a cetain range of values,the existence of positive solutions are obtained by using global bifurcation theorem.

关 键 词：四阶ODE 正解 分歧理论 Krein-Rutman定理 

分 类 号：O175.14[理学—数学] O175.8[理学—基础数学]