We investigate normalized solutions to a class of Chern-Simons-Schrödinger systems with combined nonlinearities f(u)=|u|p−2u+µ|u|q−2u in R2,whereµ∈{±1}and 2<p,q<∞.The solutions correspond t...We investigate normalized solutions to a class of Chern-Simons-Schrödinger systems with combined nonlinearities f(u)=|u|p−2u+µ|u|q−2u in R2,whereµ∈{±1}and 2<p,q<∞.The solutions correspond to critical points of the underlying energy functional subject to the L2-norm constraint,namely,∫R2|u|2dx=c for c>0 given.Of particular interest is the competing and double L2-supercritical case,i.e.,µ=−1 and min{p,q}>4.We prove several existence and multiplicity results depending on the size of the exponents p and q.It is worth emphasizing that some of them are also new even in the study of the Schrödinger equations.In addition,the asymptotic behavior of the solutions and the associated Lagrange multipliersλas c→0 is described.展开更多
Using the Faddeev-Jackiw （FJ） quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which ...Using the Faddeev-Jackiw （FJ） quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which agree with the results obtained by using the Dirac＇s method.展开更多
In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e^(2)|A|^(2)+(V(x)+2eA_(0))+2(1+κq/2)N]u+q|u|^(p−2)u=0,−ΔN+κ^(2)q^(2)N+q(1+κq2)u^(2)=0,κ(∂_(1)A_(2)−∂_(2)A_(1))=−eu^(2),∂_(1)A_(1)+∂_(2)A_(2)=0,...In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e^(2)|A|^(2)+(V(x)+2eA_(0))+2(1+κq/2)N]u+q|u|^(p−2)u=0,−ΔN+κ^(2)q^(2)N+q(1+κq2)u^(2)=0,κ(∂_(1)A_(2)−∂_(2)A_(1))=−eu^(2),∂_(1)A_(1)+∂_(2)A_(2)=0,κ∂_(1)A_(0)=e^(2)A_(2)u^(2),κ∂_(2)A_(0)=−e^(2)A_(1)u^(2),where u∈H^(1)(R^(2)),p∈(2,4),Aα:R^(2)→R are the components of the gauge potential(α=0,1,2),N:R^(2)→R is a neutral scalar field,V(x)is a potential function,the parametersκ,q>0 represent the Chern-Simons coupling constant and the Maxwell coupling constant,respectively,and e>0 is the coupling constant.In this paper,the truncation function is used to deal with a neutral scalar field and a gauge field in the Chern-Simons-Schrödinger problem.The ground state solution of the problem(P)is obtained by using the variational method.展开更多
基金supported by National Natural Science Foundation of China (Grant No.12071486)supported by National Natural Science Foundation of China (Grant No.11671236)Shandong Provincial Natural Science Foundation (Grant No. ZR2020JQ01)。
文摘We investigate normalized solutions to a class of Chern-Simons-Schrödinger systems with combined nonlinearities f(u)=|u|p−2u+µ|u|q−2u in R2,whereµ∈{±1}and 2<p,q<∞.The solutions correspond to critical points of the underlying energy functional subject to the L2-norm constraint,namely,∫R2|u|2dx=c for c>0 given.Of particular interest is the competing and double L2-supercritical case,i.e.,µ=−1 and min{p,q}>4.We prove several existence and multiplicity results depending on the size of the exponents p and q.It is worth emphasizing that some of them are also new even in the study of the Schrödinger equations.In addition,the asymptotic behavior of the solutions and the associated Lagrange multipliersλas c→0 is described.
文摘Using the Faddeev-Jackiw （FJ） quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which agree with the results obtained by using the Dirac＇s method.
基金partially supported by NSFC (12161044)Natural Science Foundation of Jiangxi Province (20212BAB211013)+1 种基金Benniao Li was partially supported by NSFC (12101274)Doctoral Research Startup Foundation of Jiangxi Normal University (12020927)
文摘In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e^(2)|A|^(2)+(V(x)+2eA_(0))+2(1+κq/2)N]u+q|u|^(p−2)u=0,−ΔN+κ^(2)q^(2)N+q(1+κq2)u^(2)=0,κ(∂_(1)A_(2)−∂_(2)A_(1))=−eu^(2),∂_(1)A_(1)+∂_(2)A_(2)=0,κ∂_(1)A_(0)=e^(2)A_(2)u^(2),κ∂_(2)A_(0)=−e^(2)A_(1)u^(2),where u∈H^(1)(R^(2)),p∈(2,4),Aα:R^(2)→R are the components of the gauge potential(α=0,1,2),N:R^(2)→R is a neutral scalar field,V(x)is a potential function,the parametersκ,q>0 represent the Chern-Simons coupling constant and the Maxwell coupling constant,respectively,and e>0 is the coupling constant.In this paper,the truncation function is used to deal with a neutral scalar field and a gauge field in the Chern-Simons-Schrödinger problem.The ground state solution of the problem(P)is obtained by using the variational method.
