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

(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.