Abstract
Via the variational methods, we prove the existence of a nontrivial solution to a singular semilinear elliptic equation with critical Sobolev‐Hardy exponent under certain conditions.
Highlights
In this paper, we consider the following elliptic problem: −∆u − μ u |x|2 =|u|2∗(s)−2 |x|s u + a(x)|u|r−2 u λu, x ∈ RN, (1.1)wc2r)hiteiisrceatlhNSeo≥cbroi3tli,ecv0ale≤xSpoμob
We prove the existence of a nontrivial solution to a singular semilinear elliptic equation with critical Sobolev-Hardy exponent under certain conditions
B2l = {x ∈ RN, |x| < 2l} ⊂ G with l > 0 and G is the domain in hypothesis (A), let 0 ≤ φ ≤ 1 be a cutting-off function in C0∞(RN ) Hr, such that φ(x) = 1 in Bl and φ(x) = 0 in RN \ B2l
Summary
We prove the existence of a nontrivial solution to a singular semilinear elliptic equation with critical Sobolev-Hardy exponent under certain conditions. 1. Introduction In this paper, we consider the following elliptic problem: Problem (1.1) has at least a nontrivial solution in Hr. Throughout this paper, we will use the letter C to denote the natural various constants independent of u, and ·dx instead of RN ·dx.
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