摘要
讨论了有界区域上的Dirichlet问题正解的存在性。通过对达到临界Sobolev嵌入最优常数的极值函数带权L2n/n-2范数的细致估计,克服了失去紧性的困难,因此得到了正解的存在性。本文对Q(x)的限制是较弱的。
By variational methods, a theorem concerning the existence of positive solutions of the Dirichlet problem -△u = Q(x)un+2/n-2 + μuq,in Ω;u = 0,on Ω is obtained, where 1 < q <
n+2/n-2 ,n≥3,μ>0 is a real constant ,and Q(x) is a nonnegative nontrivial bounded measurable func-
tion. Furthermore, we assume that Q(x) attains its essential supermum at x0 ∈Ω and |Q(x) - Q(x0)| = 0( |x - X0|) al x = XQ. The results are new,and the restriction of Q(x) is very weak.
出处
《重庆大学学报（自然科学版）》
EI
CAS
CSCD
1991年第3期96-100,共5页
Journal of Chongqing University
关键词
半线性
椭圆型方程
正解
变分法
variational method
semilinear elliptic equation / positive solution
critical Sobolev exponent
