三阶非线性系统三点边值问题的正解(英文)  

Positive solutions to three-point boundary value problems for third order nonlinear systems

作　　者：何希萍[1,2] 孙红蕊[2] 

机构地区：[1]甘肃广播电视大学教学指导中心,兰州730030 [2]兰州大学数学与统计学院,兰州730000

出　　处：《兰州大学学报（自然科学版）》2010年第4期84-88,96,共6页Journal of Lanzhou University(Natural Sciences)

基　　金：Supported by the National Natural Science Foundation of China(10801065);Natural Science Foundation of Gansu province(0803RJZA096)

摘　　要：研究了三阶非线性系统u′″(t)=f(t,u(t)),t∈[t_1,t_3]在满足边值条件u(t_1)=u′(t_2)=0,γu(t_3)+δu″(t_3)=0下正解的存在性,其中u=(u_1,…,u_n),γ=diag[γ_1,…,γ_n],δ=diag[δ_1,…,δ_n].运用Leray-Schauder型非线性抉择和Krasnosel'skii不动点定理,建立了此问题单个和两个正解的存在性结果,并举例说明了所得结论的有效性.The existence of positive solutions was studied for third order nonlinear system u＇＇＇（t）=f（t,u（t））,t∈[t1,t3] with the boundary conditions u（t1）=u＇（t2）=0, δu＇＇（t3）=0, where u=（u1,…,un）,γ=diag[γ1,…,γn],δ=diag[δ1,…,δn]. Some results were obtained for the existence of single and twin positive solutions for the above system by using nonlinear alternative of Leray-Schauder type and Krasnosel＇skii fixed point theorem in a cone. An example was also given to illustrate the main results.

关 键 词：非线性系统 三点边值问题 正解 不动点 

分 类 号：O175.14[理学—数学]