山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (9): 69-75.doi: 10.6040/j.issn.1671-9352.0.2016.506
闫东亮
YAN Dong-liang
摘要: 获得了非线性函数带有导数项的二阶周期边值问题{u″(t)+au(t)=f(t,u(t),u'(t)),〓t∈[0,1],u(0)=u(1), u'(0)=u'(1)正解的存在性, 其中(π2)/4π2, f:[0,1]×R+×R→R+连续。 f(t,x,y)满足Nagumo条件, 且关于 x 和 y 满足一定的超线性增长条件。针对超线性情形, Nagumo条件关于y严格控制了f的增长。主要结果的证明基于不动点指数理论。
中图分类号:
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