| 非线性奇异微分方程周期解的存在性和多重性 |
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| 引用本文： | 邓翠容.非线性奇异微分方程周期解的存在性和多重性[J].怀化学院学报,2009,28(11):1-5. |
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| 作者姓名： | 邓翠容 |
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| 作者单位： | 怀化学院数学系,湖南,怀化,418008 |
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| 摘 要： | 利用变分法研究非线性奇异微分方程(g(t)|u′(t)|p-2u′(t))′-|u(t)|p-2u(t)=λF(t,u(t)),a.e.t∈0,T]u(0)-u(T)=gq-1(0)u′(0)-gq-1(T)u′(T)=0(P)周期解的存在性和多重性问题,其中T>0,λ>0,g∈L∞(0,T;R+),ess.infg>0,p2,1p+1q=1,F:0,T]×RN→R满足下面的假设:(A)对任意的u∈RN,F(t,u)关于t可测;对几乎所有的t∈0,T],F(t,u)关于u连续可微.并且存在a∈C(R+,R+),b∈L1(0,T;R+),使得对一切的u∈RN,几乎所有的t∈0,T],有|F(t,u)|a(|u|)b(t),|F(t,u)|a(|u|)b(t).
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| 关 键 词： | 临界点 周期解 非线性奇异微分方程 |
The Existence and Multiplicity of Periodic Solutions for the Nonlinear Singular Differential Equation |
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| DENG Cui-rong.The Existence and Multiplicity of Periodic Solutions for the Nonlinear Singular Differential Equation[J].Journal of Huaihua University,2009,28(11):1-5. |
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| Authors: | DENG Cui-rong |
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| Institution: | DENG Cui-rong(Department of Mathematics,Huaihua University,Huaihua,Hunan 418008) |
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| Abstract: | In this paper,wu use the variational method to study the existence and multiplicity of periodic solutions for the nonlinear singular differential equation(g(t)|u'(t)|p-2u'(t))'-|u(t)|p-2u(t)=λF(t,u(t)),a.e.t∈0,T]u(0)-u(T)=gq-1(0)u'(0)-gq-1(T)u'(T)=0where T>0,λ>0,g∈L∞(0,T;R+),ess.inf g>0,p2,1p+1q=1,and F:0,T]×RN→R satisfies the following assumption:(A)F(t,u) is measurable in t for every u∈RN and continuously differential in u for a.e.t∈0,T] and there exist a∈C(R+,R+),b∈L1(0,T;R+) such that|F(t,u)|a(|u|)b(t),|F(t,u)|a(|u|)b(t)for all u∈RN and a.e.t∈0,T]. |
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| Keywords: | critical point periodic solution nonlinear singular differential equation |
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