1-维次线性p-Laplacian方程的无穷多周期解

Large Multiple Periodic Solutions for the 1-Dimensional Sub-Linear p-Laplacian Equation

该文研究1-维p-Laplacian方程(|x′|^(p−2)x′)′+f(t,x)=0end{document}周期解的存在性和多解性,其中f(t,x)满足原点附近的次线性条件,即lim∣x∣→0f(t,x)∣x∣^(p−2)x=0.得到的存在性结果可以应用于经典方程x′′+f(t,x)=0.证明方法基于Poincaré-Birkhoff扭转定理.

In this paper,we obtain existence and multiplicity of periodic solutions for 1-dimensional p-Laplacian equation(|x′|^(p−2)x′)′+f(t,x)=0,where f∈C(R×R,R)is 2π-periodic in the first variable and satisfies the assumption f(t,x)∣x∣^(p−2)x→0,as∣x∣→0.The new existence results can be applied to situations in which the more classical equation x′′+f(t,x)=0.Proofs are based on Poincaré-Birkhoff twist theorem.