动力系统方法应用到一类非线性椭圆方程的基态解

Ground States of Nonlinear Elliptic Equations:A Dynamical Approach

本文将动力系统理论的思想和方法应用到一类具有Sobolev次临界指数的非线性椭圆型方程,通过吸引子的存在性及其结构分析来研究稳态方程基态解的存在性及其渐近性态.这一方法的细致应用,不仅需要在理论和应用上创新,而且必将为相关领域的研究提供新的研究途径和思想方法,对非线性分析和无穷维动力系统的理论和应用发展产生积极的推动作用.

In this paper,we apply the ideas and methods of dynamical system theory to a class of nonlinear elliptic equation with subcritical exponent.We study the existence and asymptotic behavior of ground state solutions of stationary equations through the existence and structure analysis of attractors.The detailed application of this method not only needs the innovation in theory and application,but also provides new ideas and methods in the related fields,especially promotes the development,in both theory and application,of nonlinear analysis and infinite-dimensional dynamical systems.