应用纤维方法研究椭圆型偏微分方程的边值问题

The study of elliptic equation with boundary value problem via fibering method

椭圆型偏微分方程的边值问题的研究无论是理论上还是应用上都有很重要的意义,考虑零边值问题-Δu=λu+|u|p-2u,x∈Ω,其中,Ω为有界区域,对上述方程已有很多著名的研究结果,但是一般采用的多为变分方法.本文转换研究方法,应用最新的纤维方法同样得到了解的存在性结果.

The study of the elliptic equation with boundary value problem is very important not only in theory but also in application, In this paper,it studys the existence of the equation -△μ=λμ＋μ^p-2μ,x∈Ωwith the zero boundary value problem invol-ving critical exponent, ~ is the bounded domain. Regarding to the above equation, we have gotten many famous results, in general via the variational method. Now in this pa- per, we transform the method and still get the existence of the above equation via the latest fibering method.