一种关于critical value在时间周期哈密顿系统里存在性的PDE证法

A PDE Approach to the Existence of the Critical Value in Time-periodic Hamiltonian System

本文主要运用PDE方法,在时间1-周期的哈密顿函数H(x,t,p)关于(x,t,p)连续,关于p凸且关于p强制、关于t线性的条件下,证明了存在一个常数c(critical value),使得u(x,t)?ct有界,其中u(x,t)是Hamilton-Jacobi方程ut+H(x,t,Dxu)=0的黏性解.

We are devoted to proving that there exists a constant c such thatu(x,t)-ct is bounded with PDE method,where u(x,t)is the viscosity solution of Hamilton-Jacobi equation ut+H(x,Dxu)=0,if the time 1-periodic Hamiltonian H(x,t,p)is continuous in(x,t,p),convex and coercive in p,and linear in t.