摘要
In this paper, when μ 〈 1/4, and 2 〈 q 〈 2(3- σ),0 ≤ σ ≤ 2 we discuss the existence of the solution for a nonlinear elliptic equation by an improved Sobolev-Hardy inequality. We also proved that the constant is optimal in the improved Sobolev-Hardy inequality. We also prove that the problem has no nontrivial solution when │y│ 〈 R, μ 〉 0 and q = 2(3- σ), the method is coming from the idea of Pohozaev.
In this paper, when μ 〈 1/4, and 2 〈 q 〈 2(3- σ),0 ≤ σ ≤ 2 we discuss the existence of the solution for a nonlinear elliptic equation by an improved Sobolev-Hardy inequality. We also proved that the constant is optimal in the improved Sobolev-Hardy inequality. We also prove that the problem has no nontrivial solution when │y│ 〈 R, μ 〉 0 and q = 2(3- σ), the method is coming from the idea of Pohozaev.
基金
Supported by NSFC (10171032).