非线性四阶周期边值问题正解的存在性和多重性  

Existence and Multiplicity of Positive Solutions of Nonlinear Fourth-order Periodic Boundary Value Problems

作　　者：杨和[1] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《大学数学》2011年第5期33-38,共6页College Mathematics

摘　　要：研究了四阶两参数常微分方程周期边值问题{u(4)(t)-βu″(t)+αu(t)=f(t,u(τ(t))),t∈[0,1],u(i)(0)=u(i)(1),i=1,2,3正解的存在性、多重性和不存在性.在非线性项f(t,u)变号的情形下,用锥上的不动点指数理论证明了该问题至少n个甚至无穷多个正解的存在性,并且获得了该问题正解的不存在性定理.The existence, multiplicity and nonexistence results of positive solutions are obtained for a nonlinear fourth-order periodic boundary value problem Under sign-changing nonlinear term f（t,u） , we prove that the problem has at least n and even infinite many positive solutions. At last, a nonexistence theorem has been obtained. The proof relies on fixed point index theorem in eone.

关 键 词：存在性 多重性 无穷多个正解 不存在性 变号非线性项 

分 类 号：O175.15[理学—数学]