一类含Caffarelli-Kohn-Nirenberg不等式的奇异椭圆型方程极小解的存在性

Existence of a Minimal Solution for a Singular Elliptic Problems Involving Caffarelli-Kohn-Nirenberg Inequalities

研究了一类带奇异项及临界指数的椭圆型方程-div(|x|-2a▽u)-μu/(|x|2(1+a))=(|u|p-2u)/(|x|bp)+λ(|u|q-2u)/(|x|dD),利用Ekeland变分原理证明了存在常数Λ>0,使得当λ∈(0,Λ)时,方程存在极小能量解.

In this paper, we investigate the singular elliptic equation -div（｜x｜^-2a△u）-μ u/｜x｜^2（1＋a）=｜μ｜p-2u/｜x｜bp＋λ｜u｜q-2u/｜x｜dD,Using the Ekeland＇ s variational principle , we prove that there exists a ∧〉0 such that for any λ∈（0,∧）, and the existence of a local minimal solution is established.