一类带临界指数的Kirchhoff型问题正基态解的存在性

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

研究了一类带临界指数的Kirchhoff型方程■其中Ω■R^(N)(N≥3)是一个具有光滑边界?Ω的有界区域,a,λ>0,b≥0,0<m<2/N-2,2<q<2m+2,2^(*)=2N/N-2为参量.利用山路引理获得了该问题正解的存在性.进一步,利用Nehari方法获得该问题正基态解的存在性.该结果补充并完善了近期相关结果.

The following Kirchhoff type equations with critical exponent■whereΩ■R^(N)(N≥3)is a smooth bounded domain with smooth boundary?Ω,a,λ>0,b≥0,0<m<2/N-2,2<q<2 m+2,2^(*)=2 N/N-2 are parameters,are considered.By using the Moutain-Pass Theorem,the existence positive solutions is obtained.Moreover,the existence positive ground state solutions is obtained by the Nehari method.Our result completes and improves the recent corresponding results in the literature.