研究了非线性项中含有时滞导数项的二阶中立型泛函微分方程（u（t）-cu（t-δ））"+a（t）u（t）=f（t,u（t）,u（t-τ（t））,u'（t-γa（t）））正周期解的存在性,获得了该方程存在正周期解和不存在正周期解的本质条件.这些条件是由系数函数a（t）与非线性项f（t, x, y, z）的关系描述的.我们的讨论基于正算子扰动方法与锥上的不动点指数理论.
Abstract
This paper deals with the existence of positive ω-periodic solutions for the second-order neutral functional differential equation with a delayed derivative term in nonlinearity (u(t)-cu(t-δ))"+a(t)u(t)=f(t,u(t),u(t-τ(t)),u'(t-γa(t))) The essential conditions on the existence and nonexistence of positive periodic solutions of the equation are obtained. The conditions concern with the relation of the coefficient function a(t) and nonlinearity f(t, x, y, z).Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.
关键词
中立型泛函微分方程 /
正周期解 /
凸锥 /
不动点指数
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Key words
neutral functional differential equation /
positive periodic solution /
cone /
fixed point index
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参考文献
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脚注
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基金
国家自然科学基金资助项目（11261053，11061031）；甘肃省自然科学基金资助项目（1208RJZA129）
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