一类带参数的四阶两点边值问题的多解性  

Existence and multiplicity of solutions for a class of fourth-order twopoint boundary value problems with parameters

作　　者：张建梅 李杰梅 ZHANG Jianmei;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,甘肃兰州730070

出　　处：《中山大学学报（自然科学版）》2020年第6期163-169,共7页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11801243);国家自然科学基金(61863022);甘肃省自然科学基金(1308RJ⁃ZA113);甘肃省高校基本科研业务费基金(2120840);甘肃省高等学校创新能力提升项目(2019B-054)。

摘　　要：研究一类带参数的四阶两点边值问题{u^(4)(t)+βu″(t)-αu(t)=f(t,u(t)),t∈(0,1)u(0)=u(1)=u″(0)=u″(1)这里参数α,β∈R且α≥-β^2/4,β<2π^2,α/π^4+β/π^2<1。在非线性项f满足一定的条件下,运用Leggett-Williams不动点定理,获得所讨论问题至少三个非负解的存在性结果。A class of fourth-order two-point boundary value problems with parameters{u(4)(t)+βu″(t)-αu(t)=f(t,u(t)),t∈(0,1)u(0)=u(1)=u″(0)=u″(1)are studied,where the parametersα,β∈R and α≥-β2/4,β<2/π^2,α/π^4+β/π^2<1.Under certain conditions of the nonlinear term f,the existence of at least three non-negative solutions for the discussed problem are obtained by using fixed point results of Leggett-Williams type.

关 键 词：四阶 多解性 LEGGETT-WILLIAMS不动点定理 

分 类 号：O175.8[理学—数学]