| 一类次二次四阶半线性微分方程两个非平凡周期解的存在性研究 |
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| 引用本文： | 冯培娟,李成岳,张卫杰.一类次二次四阶半线性微分方程两个非平凡周期解的存在性研究[J].中央民族大学学报(自然科学版),2012,21(1):80-83,87. |
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| 作者姓名： | 冯培娟 李成岳 张卫杰 |
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| 作者单位： | 1. 中央民族大学理学院,北京,100081
2. 中央民族大学附属中学,北京,100081 |
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| 摘 要： | 这篇文章应用临界点理论中的Brezis-Nirenberg型环绕定理,证明了一类四阶半线性次二次微分方程u(4)-Au″-Bu-Vu(t,u)=0(1),两个非平凡2T-周期解的存在性.其中A0,B0,Aπ2BT2,V(t,u)∈C1(0,T]×R,R)满足条件2V(t,u)-uV(t,u)→∞,|u|→∞,t∈0,T].
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| 关 键 词： | Brezis-Nirenberg型环绕定理 周期解 四阶微分方程 |
Existence of Two Nontrivial Periodic Solutions for a Class of Subquadratic Semi-linear Forth-Order Differential Equations |
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| FENG Pei-juan,LI Cheng-yue,ZHANG Wei-jie.Existence of Two Nontrivial Periodic Solutions for a Class of Subquadratic Semi-linear Forth-Order Differential Equations[J].Journal of The Central University for Nationalities(Natural Sciences Edition),2012,21(1):80-83,87. |
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| Authors: | FENG Pei-juan LI Cheng-yue ZHANG Wei-jie |
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| Institution: | 2(College of Science,Minzu Unive,rsity of China,Beijing 100081,China) |
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| Abstract: | Existence of two nontrivial Periodic Solutions for a class of subquadratic semi-linear forth-order differential equations u(4)-Au″-Bu-Vu(t,u)=0 is studied by the local linking theorem due to Brezis and Nirenberg,where A>0,B>0,Aπ2>BT2,V(t,u)∈C1(0,T]×R,R) satisfies 2V(t,u)-uVu(t,u)→-∞,|u|→∞,t∈0,T]. |
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| Keywords: | brezis-nirenberg’s linking theorem periodic solutions forth-order differential equations |
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