| 一类Lienard型p-Laplacian方程周期解的存在唯一性 |
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| 引用本文： | 陈仕洲.一类Lienard型p-Laplacian方程周期解的存在唯一性[J].数学的实践与认识,2013,43(8). |
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| 作者姓名： | 陈仕洲 |
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| 作者单位： | 韩山师范学院数学与应用数学系,广东潮州,521041 |
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| 摘 要： | 利用重合度理论和一些分析技巧,研究了一类Lienard型p-Laplacian方程(φ_p(x((n-1))(t)))'+f(t,x(t),x((n-1))(t)))'+f(t,x(t),x((n-1))(t))+(?)gk(t,x(t),x(t-τ_k(t))=e(t)获得其存在周期解的充分条件,并给出了在p≥2,n=2,f(t,u,v)=h(t,v)情形下存在唯一周期解的充分条件.所用方法与已有文献不同,结果是新的且与时滞τ_k(t)有关.
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| 关 键 词： | p-Laplacian方程 周期解 Lienard方程 重合度理论 |
Existence and Uniquenees of Periodic Solutions for a Kind of Lienard Type p-Laplacian Equation |
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| CHEN Shi-zhou.Existence and Uniquenees of Periodic Solutions for a Kind of Lienard Type p-Laplacian Equation[J].Mathematics in Practice and Theory,2013,43(8). |
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| Authors: | CHEN Shi-zhou |
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| Abstract: | By using the continuation theorem of coincidence degree and some analysis techniques, we study a kind of Lienard type p-Laplacian equation (φ_p(x~(n-1)(t)) ) +f(t,x(t),x~(n-1)(t)) +(?)gk(t,x(t),x(t -τ_k(t)) = e(t) Some new sufficient conditions for the existence of periodic solutions,the existence and uniquenees in the case thatp≥2,n = 2,f(t,u,v) = h(t,v)axe obtained.The method is different from the previous literatures,the results is new and related with delaysτ_k(t). |
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| Keywords: | p-Laplacian equation periodic solution Lienard equation coincidence degree |
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