This article deals with the problem-△pu=λ｜u｜p/-2｜x｜pIn^p R/｜x｜＋f（x,u）,x∈Ω;u=0,x∈δΩ,where n = p. The authors prove that a Hardy inequality and the constant （p/p-1）^p is optimal. They also prove the ex...This article deals with the problem-△pu=λ｜u｜p/-2｜x｜pIn^p R/｜x｜＋f（x,u）,x∈Ω;u=0,x∈δΩ,where n = p. The authors prove that a Hardy inequality and the constant （p/p-1）^p is optimal. They also prove the existence of a nontrivial solution of the above mentioned problem by using the Mountain Pass Lemma.展开更多
In this paper, we study the existence result for degenerate elliptic equations with singular potential and critical cone sobolev exponents on singular manifolds. With the help of the variational method and the theory ...In this paper, we study the existence result for degenerate elliptic equations with singular potential and critical cone sobolev exponents on singular manifolds. With the help of the variational method and the theory of genus, we obtain several results under different conditions.展开更多
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
基金Supported by NSFC(10471047)NSF Guangdong Province(04020077)
文摘This article deals with the problem-△pu=λ｜u｜p/-2｜x｜pIn^p R/｜x｜＋f（x,u）,x∈Ω;u=0,x∈δΩ,where n = p. The authors prove that a Hardy inequality and the constant （p/p-1）^p is optimal. They also prove the existence of a nontrivial solution of the above mentioned problem by using the Mountain Pass Lemma.
文摘In this paper, we study the existence result for degenerate elliptic equations with singular potential and critical cone sobolev exponents on singular manifolds. With the help of the variational method and the theory of genus, we obtain several results under different conditions.
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.
