一类具有可变号系数的p-Laplace方程周期解的存在性

Existence of Periodic Solutions for a Kind of p-Laplacian Equations with Variable Coefficients

研究了如下一类p-Laplace微分方程(φp(x'(t)))'+β(t)g(x(t))=e(t)周期解的存在性问题,其中β(t)在区间[0,T]上可以变号,并且允许∫T0β(t)dt=0,这与已有的结论是不同的。通过应用临界点理论,获得了一个新结果。最后,通过一个例子和几个注解来说明理论结果的有效性。

The existence of periodic solutions for a kind of p-Laplacian equations is studied,such as ψρ（x＇（t）））＇ ＋β（t）g（x（t）） =e（t）,where β（t） can change sign over [0,T],and ∫0Tβ（t）dt =0 is possible.Such problem is different from the previous research results.Depending on the critical point theory we obtain a new result for such problem.Moreover,an example and some remarks are presented to verrify the theoretical results.