一类p-Laplacian-Rayleigh方程周期正解的存在性

Existence of positive periodic solution for a kind of p-Laplacian-Rayleigh equations

用重合度定理讨论一类具奇性的p-Laplacian-Rayleigh方程(|x'|p-2x')'+f(x')+g(t,x)=0周期正解的存在性问题,其中p>1,f:R→R为任意连续函数,g(t,x):R×(0,+∞)→R连续,且在x=0处具有奇性。假设f小于指数增长,证明此类p-Laplacian-Rayleigh方程至少存在一个周期正解,给出周期正解存在的充分条件。应用文中定理,证明两类方程存在周期正解。

Coincidence degree theorem is used to study the existence of positive periodic solutions of the p-Laplacian-Rayleigh equations of the form（ ｜ x＇ ｜p- 2x＇） ＇ ＋ f（ x＇） ＋ g（ t,x） = 0with p 1,f： R→R is an arbitrary continuous function,g（ t,x） ： R ×（ 0,＋ ∞） →R is continuous and singular at x = 0. A sufficient condition is given in the case that f is less than exponential growth such that the class of p-Laplacian-Rayleigh equations has at least one positive periodic solution. At last,two examples are offered to show the applicability of the conclusion.