This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes...This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes the unit outward normal to boundary aΩ. By vaxiational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.展开更多
This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ...This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ is the spectrum of the operator -△-μI/|x|2 with zero Dirichlet boundary condition, 0 <μ< μ-,μ-=(N-2)2/4, f(x,u)is an asymmetric lower order perturbation of |u|2* -1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.展开更多
文摘This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes the unit outward normal to boundary aΩ. By vaxiational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.
文摘This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ is the spectrum of the operator -△-μI/|x|2 with zero Dirichlet boundary condition, 0 <μ< μ-,μ-=(N-2)2/4, f(x,u)is an asymmetric lower order perturbation of |u|2* -1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.
