非线性项变号情形下四阶周期边值问题解的存在性  

Existence of Solutions to a Fourth-order Periodic Boundary Value Problem with Sign-changing Nonlinear Terms

作　　者：李俊杰[1] 陈东亮 

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 [2]平阳市庄浪县第三中学,甘肃平阳744600

出　　处：《郑州大学学报（理学版）》2011年第1期20-24,共5页Journal of Zhengzhou University:Natural Science Edition

基　　金：甘肃省自然科学基金资助项目;编号0710RJZA103;西北师范大学创新工程基金资助项目;编号NWNU-KJCXGC-3-47

摘　　要：考虑四阶周期边值问题{u(4)(t)-βu″(t)+αu(t)=f(t,u(t)),0<t<1u(i)(0)=u(i)(1),i=0,1,2,3解的存在性,其中非线性项f∶[0,1]×R→R连续,可变号或可取负.在对f不作任何非负性假设的条件下,主要利用相关线性算子的第一特征值和拓扑度理论,建立了问题解的存在性结果.The existence of solutions to the following fourth-order periodic boundary value problem,{u（4）（t）-βu″（t）＋αu（t）=f（t,u（t））,0t1u（i）（0）=u（i）（1）,i=0,1,2,3 was studied,where nonlinear term f∶×R→R was continuous,took negative values and was sign-changing.Without making any nonnegative assumption of f,by using the first eigenvalue corresponding to the relevant linear operator and the topological degree theory,the existence results to the above periodic boundary value problem was established.

关 键 词：四阶周期边值问题 谱半径 拓扑度理论 不动点 

分 类 号：O178.8[理学—数学]