一类带临界指数的非齐次Kirchhoff型方程正解的存在性

Existence of Positive Solutions for a Class of Nonhomogeneous Kirchhoff Type Problems with Critical Exponent

研究了一类带临界指数的非齐次Kirchhoff型方程{-(a+∫b|▽u|2dxΩ)Δu=|u|4 u+λf(x)x∈Ωu=0 x∈Ω其中Ω■R^3是一个非空有界开集;a,b,λ>0为参量;f∈L6/5(Ω)是个非零非负函数.利用变分方法获得了该方程的一个正解.

The following nonhomogeneous Kirchhoff type equations with critical exponent{-（a ＋b∫n｜▽u｜~2dx）Δu=｜u｜~4u ＋λf（x） x ∈Ωu =0x ∈Ω where Ω is a smooth bounded domain in R^3,a,b,λ0 are parameters and f∈L6/5（Ω）is nonzero and nonnegative,are considered.By the variational method,apositive solution is obtained.