In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at ...In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at least a positive radial solution is established for a class of semilinear elliptic problems involving critical Hardy-Sobolev exponent and Hardy terms. The main tools are variational method, critical point theory and some analysis techniques.展开更多
In this paper,we investigate the following p-Kirchhoff equation{∫R^(N)|u|^(2)dx=ρ,(a+b)∫RN(|Δu}^(p)+|u|^(p))dx)(-Δpu+|u|^(p-2u)=|u|^(s-2)u+μu,x∈R^(N),where a>0,b≥0,p>0 are constants,constants,p*=N-P/Np i...In this paper,we investigate the following p-Kirchhoff equation{∫R^(N)|u|^(2)dx=ρ,(a+b)∫RN(|Δu}^(p)+|u|^(p))dx)(-Δpu+|u|^(p-2u)=|u|^(s-2)u+μu,x∈R^(N),where a>0,b≥0,p>0 are constants,constants,p*=N-P/Np is the critical Sobolev exponent,μis a Lagrange multiplier,-Δpu=-div(|Δu|_(p-2)u),2<p<N2p,μ∈R,and s∈(2N/N+2p-2,p*).We demonstratethat he p-Kirchhoff equation has a normalized solution using the mountain pass lemma and some analysis techniques.展开更多
文摘In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at least a positive radial solution is established for a class of semilinear elliptic problems involving critical Hardy-Sobolev exponent and Hardy terms. The main tools are variational method, critical point theory and some analysis techniques.
基金supported by Natural Science Foundation of Fujian Province(No.2022J013392020J01708)National Foundation Training Program of Jimei University(ZP2020057).
文摘In this paper,we investigate the following p-Kirchhoff equation{∫R^(N)|u|^(2)dx=ρ,(a+b)∫RN(|Δu}^(p)+|u|^(p))dx)(-Δpu+|u|^(p-2u)=|u|^(s-2)u+μu,x∈R^(N),where a>0,b≥0,p>0 are constants,constants,p*=N-P/Np is the critical Sobolev exponent,μis a Lagrange multiplier,-Δpu=-div(|Δu|_(p-2)u),2<p<N2p,μ∈R,and s∈(2N/N+2p-2,p*).We demonstratethat he p-Kirchhoff equation has a normalized solution using the mountain pass lemma and some analysis techniques.
