带阻尼项的(q,p)-Laplace问题周期解的存在性  

Existence of periodic solution for( q,p)-Laplace problem with a damped vibration

作　　者：万树园 王智勇[1] 

机构地区：[1]南京信息工程大学数学与统计学院,南京210044

出　　处：《黑龙江大学自然科学学报》2016年第6期735-739,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11571176)

摘　　要：(q,p)-Laplace系统是一类非常重要的微分方程模型,来自于非牛顿流体问题及非线性弹性问题。利用临界点理论中的极大极小方法,研究一类带有阻尼项的(q,p)-Laplace问题周期解的存在性。将此类问题的周期解,转化为定义在一个适当空间上能量泛函的临界点,根据鞍点定理,得到新的存在性定理。结论推广并发展了已有文献中的相关结果。（q,p） -Laplace system is a very important model of differential equation which comes from the non-Newtonian fluid problem and the nonlinear elasticity. By using max-min methods in critical point the- ory, the existence of periodic solution for a class of （q,p） -Laplace problem with damped vibration is studied. The periodic solution problem is first converted into the critical point of a functional defined on a proper space, then a new existence theorem is obtained via saddle point theorem. The existence theorem extends and improves some results in literatures.

关 键 词：周期解 (q p)-Laplace CERAMI条件 鞍点定理 

分 类 号：O175.12[理学—数学]