In this paper,we are concerned with the existence of multiple solutions to the critical magnetic Schrödinger equation(-i▽-a(x))^(2)u+⒂λV(x)u=p|u|^(p-2)u+(∫R(n)|u(y)|^(2)_(a)^(*)/|x-y|^(a)dy)|u|2_(a)^(*)-2_(u)...In this paper,we are concerned with the existence of multiple solutions to the critical magnetic Schrödinger equation(-i▽-a(x))^(2)u+⒂λV(x)u=p|u|^(p-2)u+(∫R(n)|u(y)|^(2)_(a)^(*)/|x-y|^(a)dy)|u|2_(a)^(*)-2_(u)in R^(N),(0.1)where N≥4,2≤p<2^(*),2_α^(*)=(2N-α)/(N-2)with 0<α<4,λ>0,μ∈R,A(x)=(A_(1)(x),A_(2)(x),…,A_(N)(x))is a real local Hölder continuous vector function,i is the imaginary unit,and V(x)is a real valued potential function on R^(N).Supposing thatΩ=int V^(-1)(0)■R^(N)is bounded,we show that problem(0.1)possesses at least cat_(Ω)(Ω)nontrivial solutions ifλis large.展开更多
The fundamental importance of sex lies in the need for reproduction and species continuity. For humans, sexual expression is an important source of physical pleasure and emotional intimacy. Healthy sexual expression i...The fundamental importance of sex lies in the need for reproduction and species continuity. For humans, sexual expression is an important source of physical pleasure and emotional intimacy. Healthy sexual expression is closely related to well-being, health and overall quality of life in both men and women. Sexual activity is also considered an important determinant of quality of life. At present, questions about sex are still largely ignored in routine consultations in almost all medical specialties. The factors affecting sexual activity are complex and can be divided into the influence of bio-psycho-sociological factors. Biological influences include anthropometric parameters, sexual function, lifestyle, neuroendocrine system, and diseases;psychological influences include psychological status, mental illness, and sexual attitudes;sociological influences include factors such as marriage, occupation, and economic status. With the epidemic and outbreak of Coronavirus disease 2019 (COVID-19), people’s way of life and work has changed, which also has a great impact on sexual activities. This article will provide a systematic review of factors related to male sexual activity.展开更多
In this paper,we deal with the existence and concentration of normalized solutions to the supercritical nonlinear Schrodinger equation {-Δu+V(x)u=μ_(q)u+a|u|^(q)u in R^(2),∫_(R^(2))|u|^(2)dx=1,where μ_(q) is the L...In this paper,we deal with the existence and concentration of normalized solutions to the supercritical nonlinear Schrodinger equation {-Δu+V(x)u=μ_(q)u+a|u|^(q)u in R^(2),∫_(R^(2))|u|^(2)dx=1,where μ_(q) is the Lagrange multiplier.We show that for q>2 close to 2,the problem admits two solutions:one is the local minimal solution u_(q) and the other one is the mountain pass solution v_(q).Furthermore,we study the limiting behavior of u_(q) and v_(q) when q→2_(+).Particularly,we describe precisely the blow-up formation of the excited state v_(q).展开更多
In this paper,we consider the following fractional Schrodinger-Poisson problem:{ε^2s(-Δ)^su+V(x)u+φu=|u|^p-1u,x∈R^N,(-Δ)^tφ=u^2,x∈R^N,where ε>0 is a small parameter,N≥3 and V(x)is a potential function.We c...In this paper,we consider the following fractional Schrodinger-Poisson problem:{ε^2s(-Δ)^su+V(x)u+φu=|u|^p-1u,x∈R^N,(-Δ)^tφ=u^2,x∈R^N,where ε>0 is a small parameter,N≥3 and V(x)is a potential function.We construct non-radial sign-changing solutions,whose components may have spikes clustering at the local minimum point of V(x).展开更多
基金supported by the National Natural Science Foundation of China(12171212)。
文摘In this paper,we are concerned with the existence of multiple solutions to the critical magnetic Schrödinger equation(-i▽-a(x))^(2)u+⒂λV(x)u=p|u|^(p-2)u+(∫R(n)|u(y)|^(2)_(a)^(*)/|x-y|^(a)dy)|u|2_(a)^(*)-2_(u)in R^(N),(0.1)where N≥4,2≤p<2^(*),2_α^(*)=(2N-α)/(N-2)with 0<α<4,λ>0,μ∈R,A(x)=(A_(1)(x),A_(2)(x),…,A_(N)(x))is a real local Hölder continuous vector function,i is the imaginary unit,and V(x)is a real valued potential function on R^(N).Supposing thatΩ=int V^(-1)(0)■R^(N)is bounded,we show that problem(0.1)possesses at least cat_(Ω)(Ω)nontrivial solutions ifλis large.
文摘The fundamental importance of sex lies in the need for reproduction and species continuity. For humans, sexual expression is an important source of physical pleasure and emotional intimacy. Healthy sexual expression is closely related to well-being, health and overall quality of life in both men and women. Sexual activity is also considered an important determinant of quality of life. At present, questions about sex are still largely ignored in routine consultations in almost all medical specialties. The factors affecting sexual activity are complex and can be divided into the influence of bio-psycho-sociological factors. Biological influences include anthropometric parameters, sexual function, lifestyle, neuroendocrine system, and diseases;psychological influences include psychological status, mental illness, and sexual attitudes;sociological influences include factors such as marriage, occupation, and economic status. With the epidemic and outbreak of Coronavirus disease 2019 (COVID-19), people’s way of life and work has changed, which also has a great impact on sexual activities. This article will provide a systematic review of factors related to male sexual activity.
基金supported by National Natural Science Foundation of China(Grant Nos.11671179 and 11771300)The second author was supported by National Natural Science Foundation of China(Grant No.11701260)Natural Science Foundation of Jiangxi Province(Grant Nos.GJJ161112 and GJJ180946)。
文摘In this paper,we deal with the existence and concentration of normalized solutions to the supercritical nonlinear Schrodinger equation {-Δu+V(x)u=μ_(q)u+a|u|^(q)u in R^(2),∫_(R^(2))|u|^(2)dx=1,where μ_(q) is the Lagrange multiplier.We show that for q>2 close to 2,the problem admits two solutions:one is the local minimal solution u_(q) and the other one is the mountain pass solution v_(q).Furthermore,we study the limiting behavior of u_(q) and v_(q) when q→2_(+).Particularly,we describe precisely the blow-up formation of the excited state v_(q).
基金supported by National Natural Science Foundation of China(Grant Nos.11501264 and 11871253)the Natural Science Foundation of Jiangxi Province(Grant No.20171BCB23030)+1 种基金Jiangxi Provincial Department of Education Fundsupported by National Natural Science Foundation of China(Grant Nos.11671179 and 11771300)。
文摘In this paper,we consider the following fractional Schrodinger-Poisson problem:{ε^2s(-Δ)^su+V(x)u+φu=|u|^p-1u,x∈R^N,(-Δ)^tφ=u^2,x∈R^N,where ε>0 is a small parameter,N≥3 and V(x)is a potential function.We construct non-radial sign-changing solutions,whose components may have spikes clustering at the local minimum point of V(x).