R^N中一类p-Kirchhoff型方程正解的存在性（英文）

Existence of positive solutions for a p-Kirchhoff type equation in R^N

本文考虑了如下的p-Kirchhoff型方程[a+λ(∫RN(|"u|p+b|u|p)dx)p-1](-Δpu+b|u|p-2 u)=f(u),x∈RN,u∈W1,p(RN),u>0,x∈RN,正解的存在性问题,其中λ>0为参数,a,b为正常数,f为连续函数.利用变分方法及截断函数技巧,本文在缺少通常紧性的条件下证明了方程正解的存在性.

In this paper,existence of positive solutions for the following p-Kirchhoff type equation[a＋λ（∫RN（｜＂u｜p＋b｜u｜p）dx）p-1]（-Δpu＋b｜u｜p-2 u）=f（u）,x∈RN,u∈W1,p（RN）,u0,x∈RN are considered,whereλ0is a parameter,a,bare positive constants and fis a continuous function.By virtue of variational method and a cut-off functional technical,the existence of positive solutions with out the usual compactness condition is obtained.