Consider the following Schr？dinger-Poisson-Slater system, （P） where ω 〉 0, λ 〉 0 and β 〉 0 are real numbers, p ∈ （1, 2）. For β=0, it is known that problem （P） has no nontrivial solution if λ 〉 0 suit...Consider the following Schr？dinger-Poisson-Slater system, （P） where ω 〉 0, λ 〉 0 and β 〉 0 are real numbers, p ∈ （1, 2）. For β=0, it is known that problem （P） has no nontrivial solution if λ 〉 0 suitably large. When β 〉 0, -β/｜x｜ is an important potential in physics, which is called external Coulomb potential. In this paper, we find that （P） with β 〉 0 has totally different properties from that of β = 0. For β 〉 0, we prove that （P） has a ground state and multiple solutions if λ 〉 cp,ω, where cp,ω 〉 0 is a constant which can be expressed explicitly via ω and p.展开更多
We calculate numerically the quantum capacitance of a nanocapacitor formed of oxide-silicon layers deposited alternately with their widths following a Cantor set structure. We show that this configuration brings about...We calculate numerically the quantum capacitance of a nanocapacitor formed of oxide-silicon layers deposited alternately with their widths following a Cantor set structure. We show that this configuration brings about a nano-hybrid capacitor which allows a classical and quantum behavior depending on the Cantor generation. In addition, we propose an approximate equivalent circuit representation for the nano-hybrid capacitor.展开更多
We are concerned with the nonlinear Schrödinger-Poisson equation{−Δu+(V(x)−λ)u+ϕ(x)u=f(u),−Δϕ=u^(2),lim|x|→+∞ϕ(x)=0,x∈R^(3),(P)whereλis a parameter,V(x)is an unbounded potential and f(u)is a general nonlin...We are concerned with the nonlinear Schrödinger-Poisson equation{−Δu+(V(x)−λ)u+ϕ(x)u=f(u),−Δϕ=u^(2),lim|x|→+∞ϕ(x)=0,x∈R^(3),(P)whereλis a parameter,V(x)is an unbounded potential and f(u)is a general nonlinearity.We prove the existence of a ground state solution and multiple solutions to problem(P).展开更多
This paper is concerned with the Schrodinger-Poisson equation -△u+V(x)u+Ф(x)u=f(x,u),x∈R^(3),-△Ф=u^(2),lim|x|→+∞Ф(x)=0.Under certain hypotheses on V and a general spectral assumption,the existence and multipli...This paper is concerned with the Schrodinger-Poisson equation -△u+V(x)u+Ф(x)u=f(x,u),x∈R^(3),-△Ф=u^(2),lim|x|→+∞Ф(x)=0.Under certain hypotheses on V and a general spectral assumption,the existence and multiplicity of solutions are obtained via variational methods.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11071245,11171339 and 11201486)supported by the Fundamental Research Funds for the Central Universities
文摘Consider the following Schr？dinger-Poisson-Slater system, （P） where ω 〉 0, λ 〉 0 and β 〉 0 are real numbers, p ∈ （1, 2）. For β=0, it is known that problem （P） has no nontrivial solution if λ 〉 0 suitably large. When β 〉 0, -β/｜x｜ is an important potential in physics, which is called external Coulomb potential. In this paper, we find that （P） with β 〉 0 has totally different properties from that of β = 0. For β 〉 0, we prove that （P） has a ground state and multiple solutions if λ 〉 cp,ω, where cp,ω 〉 0 is a constant which can be expressed explicitly via ω and p.
文摘We calculate numerically the quantum capacitance of a nanocapacitor formed of oxide-silicon layers deposited alternately with their widths following a Cantor set structure. We show that this configuration brings about a nano-hybrid capacitor which allows a classical and quantum behavior depending on the Cantor generation. In addition, we propose an approximate equivalent circuit representation for the nano-hybrid capacitor.
基金supported by NSFC(11871386 and12071482)the Natural Science Foundation of Hubei Province(2019CFB570)。
文摘We are concerned with the nonlinear Schrödinger-Poisson equation{−Δu+(V(x)−λ)u+ϕ(x)u=f(u),−Δϕ=u^(2),lim|x|→+∞ϕ(x)=0,x∈R^(3),(P)whereλis a parameter,V(x)is an unbounded potential and f(u)is a general nonlinearity.We prove the existence of a ground state solution and multiple solutions to problem(P).
基金supported in part by the National Natural Science Foundation of China(Grant No.11701285)the Natural Science Foundation of Jiangsu Province(No.BK20161053).
文摘This paper is concerned with the Schrodinger-Poisson equation -△u+V(x)u+Ф(x)u=f(x,u),x∈R^(3),-△Ф=u^(2),lim|x|→+∞Ф(x)=0.Under certain hypotheses on V and a general spectral assumption,the existence and multiplicity of solutions are obtained via variational methods.
