Positive solutions for a semilinear elliptic problem with critical exponent
نویسندگان
چکیده
منابع مشابه
An Elliptic Problem with Critical Exponent and Positive Hardy Potential
where B1 = {x ∈ RN | |x| < 1} is the unit ball in RN (N ≥ 3), λ, μ > 0, 2∗ := 2N/(N − 2). When μ < 0, this problem has been considered by many authors recently (cf. [5, 6, 7, 8]). But when μ > 0, this problem has not been considered as far as we know. In fact, the existence of nontrivial solution for (1.1) when μ > 0 is an open problem which was imposed in [7]. In this paper, we get the followi...
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and Applied Analysis 3 The following Hardy-Sobolev inequality is due to Caffarelli et al. 12 , which is called Caffarelli-Kohn-Nirenberg inequality. There exist constants S1, S2 > 0 such that (∫ RN |x|−bp |u|pdx )p/p∗ ≤ S1 ∫ RN |x|−ap|∇u|pdx, ∀u ∈ C∞ 0 ( R N ) , 1.8 ∫ RN |x|− a 1 |u|dx ≤ S2 ∫ RN |x|−ap|∇u|pdx, ∀u ∈ C∞ 0 ( R N ) , 1.9 where p∗ Np/ N − pd is called the Sobolev critical exponent. ...
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications
سال: 1996
ISSN: 0362-546X
DOI: 10.1016/0362-546x(95)00059-5