This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solution...This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.展开更多
This paper is dedicated to studying the following elliptic system of Hamiltonian type:■where N≥3,V,Q∈C(RN,R),V(x)is allowed to be sign-changing and inf Q>0,and F∈C1(R2,R)is superquadratic at both 0 and infinity...This paper is dedicated to studying the following elliptic system of Hamiltonian type:■where N≥3,V,Q∈C(RN,R),V(x)is allowed to be sign-changing and inf Q>0,and F∈C1(R2,R)is superquadratic at both 0 and infinity but subcritical.Instead of the reduction approach used in Ding et al.(2014),we develop a more direct approach—non-Nehari manifold approach to obtain stronger conclusions but under weaker assumptions than those in Ding et al.(2014).We can find anε0>0 which is determined by terms of N,V,Q and F,and then we prove the existence of a ground state solution of Nehari-Pankov type to the coupled system for allε∈(0,ε0].展开更多
In this paper, we investigate nonlinear Hamiltonian elliptic system {-△u＋b（x）· u＋（V（x）＋τ）u=K（x）g（v） in R^N,-△u-b（x）· v＋（V（x）＋τ）v=K（x）f（u） in R^N,u（x）→ and v（x）→0 as ｜x｜...In this paper, we investigate nonlinear Hamiltonian elliptic system {-△u＋b（x）· u＋（V（x）＋τ）u=K（x）g（v） in R^N,-△u-b（x）· v＋（V（x）＋τ）v=K（x）f（u） in R^N,u（x）→ and v（x）→0 as ｜x｜→∞2,where N ≥ 3, τ 〉 0 is a positive parameter and V, K are nonnegative continuous functions,f and g are both superlinear at 0 with a quasicritical growth at infinity. By establishing avariational setting, the existence of ground state solutions is obtained.展开更多
基金supported by the Hunan Provincial Innovation Foundation for Postgraduate(CX2013A003)the NNSF(11171351,11361078)SRFDP(20120162110021)of China
文摘This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.
基金supported by National Natural Science Foundation of China(Grant No.11171351)
文摘This paper is dedicated to studying the following elliptic system of Hamiltonian type:■where N≥3,V,Q∈C(RN,R),V(x)is allowed to be sign-changing and inf Q>0,and F∈C1(R2,R)is superquadratic at both 0 and infinity but subcritical.Instead of the reduction approach used in Ding et al.(2014),we develop a more direct approach—non-Nehari manifold approach to obtain stronger conclusions but under weaker assumptions than those in Ding et al.(2014).We can find anε0>0 which is determined by terms of N,V,Q and F,and then we prove the existence of a ground state solution of Nehari-Pankov type to the coupled system for allε∈(0,ε0].
基金partially supported by the Honghe University Doctoral Research Program(XJ17B11)Yunnan Province Applied Basic Research for Youthsthe Yunnan Province Local University(Part)Basic Research Joint Project(2017FH001-013)
文摘In this paper, we investigate nonlinear Hamiltonian elliptic system {-△u＋b（x）· u＋（V（x）＋τ）u=K（x）g（v） in R^N,-△u-b（x）· v＋（V（x）＋τ）v=K（x）f（u） in R^N,u（x）→ and v（x）→0 as ｜x｜→∞2,where N ≥ 3, τ 〉 0 is a positive parameter and V, K are nonnegative continuous functions,f and g are both superlinear at 0 with a quasicritical growth at infinity. By establishing avariational setting, the existence of ground state solutions is obtained.
