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...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.展开更多
文摘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.
