一类完全四阶两点边值问题正解的存在性  

Existence of Positive Solutions for a Class of Complete Fourth-Order Two-Point Boundary Value Problems

作　　者：邓瑞娟[1] 崔洪瑞 DENG Rui-juan;CUI Hong-rui(Department of Basic,Wuhu Institute of Technology,Wuhu 241003,Anhui,China;GDPU Undergraduate School of Medical Business,Guangdong Pharmaceutical University,Guangzhou 510006,China)

机构地区：[1]芜湖职业技术学院基础部,安徽芜湖241003 [2]广东药科大学医药商学院,广东广州510006

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2020年第6期497-501,508,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：安徽高校自然科学研究重点资助项目(KJ2019A0976);安徽省高等学校质量工程资助项目(2017ghjc270)。

摘　　要：利用锥上的不动点指数原理,给出了一类完全四阶两点边值问题-u(4)(t)=f(t,u(t),u′(t),u″(t),u″(t)),t∈[0,1],u(0)=u′(0)=u″(0)=u″(1)=0正解的存在性。其中,f(t,x,y,z,w)关于x,y,z,w在(x,y,z,w)=x2+y2+z2+w2充分大或者充分小时,满足一些不等式条件;同时,f关于z满足Nagumo条件。Using the fixed point index principle on cone,the paper discussed the existence of positive solutions of a class of complete fourth-order two-point boundary value problems for-u(4)(t)=f(t,u(t),u′(t),u″(t),u″(t)),t∈[0,1],u(0)=u′(0)=u″(0)=u″(1)=0,where f satisfied some inequality conditions on x,y,z,w,when(x,y,z,w)=x2+y2+z2+w2 was sufficiently large or small,and f satisfied Nagumo conditions on z.

关 键 词：四阶两点 边值问题 正解 

分 类 号：O172.2[理学—数学]