带有完全非线性项的四阶边值问题的多正解性  

Existence and multiplicity of positive solutions for fourth-order boundary value problems with a fully nonlinear term

作　　者：姚燕燕 李杰梅 YAO Yanyan;LI Jiemei(School of Mathematics and Physics,Lanzhou Jiaotong University^Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《华东师范大学学报（自然科学版）》2020年第6期38-45,共8页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11801243,61863022);甘肃省高等学校创新能力提升项目(2019B-054);兰州交通大学青年科学基金(2017012)。

摘　　要：本文讨论四阶两点边值问题{u(4)(t)=f (t, u(t), u′(t), u″(t), u′′′(t)), t∈(0, 1),u(0)=u′(0)=u″(1)=u′′′(1)=0.这里非线性项f中含有项u′,u″和u′′′,因而该问题为带有完全非线性项的四阶边值问题.运用LeggettWilliams型的两个不动点定理,在f满足一定条件的情况下,获得了该问题至少存在两个或者三个正解的结果.最后举例验证了所获定理的有效性.In this paper, we discuss the fourth-order two-point boundary value problem { u(4)(t) = f(t, u(t), u′(t), u′′(t), u′′′(t)), t ∈(0, 1),u(0) = u′(0) = u′′(1) = u′′′(1)= 0.Here, the nonlinear term f contains u′, u′′ and u′′′;therefore, the problem is a fourth-order boundary value problem with a fully nonlinear term. By using the two fixed point theorems of Leggett-Williams type,the existence of at least two or at least three positive solutions are obtained under the term f that satisfies certain conditions. Finally, two examples are given to verify the theorems.

关 键 词：完全非线性项 多正解 LEGGETT-WILLIAMS不动点定理 

分 类 号：O175.8[理学—数学]