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个人简介

唐先华(Tang Xianhua),男,1963年3月出生,教授(博导),享受国务院政府特殊津贴专家,湖南省新世纪121人才工程第二层次人选。1984年7月毕业于衡阳师专物理系;1990年6月于南开大学基础数学专业研究生毕业,获硕士学位;1995年8月调入原中南工业大学数软系任教, 1997年9月考入湖南大学应用数学系,在职攻读应用数学专业泛函微分方程方向博士,于2000年6月毕业,获博士学位, 其毕业论文获湖南省2002年优秀博士论文。1998年10月晋升为副教授,2000年10月破格晋升为教授, 2002年评为博士生指导教师。2001年3月-2001年6月, 应Dr. Zou Xingfu邀请访问加拿大Newfoundland纪念大学,合作研究三个月; 2002年1月-2003年1月, 被邀请访问意大利国际理论物理中心(ICTP), 做一年期的研究员。近年来,主要研究领域是非线性分析、偏微分方程、Hamilton系统及离散动力系统,在《SIAM J. Math. Anal.》、《J. Differential Equations》、《Calc.Var.Partial Differential Equations》、《J. Dynam.Differential Equations》、《Nonlinearity》、《J. London Math. Soc.》、《Discret. Cont. Dyn. Sys.-A》、《Proc. Amer. Math. Soc.》、《Proc. Royal Soc. Edinburgh (A)》和《中国科学》等国内外许多重要刊物上发表了论文300余篇,文章SCI引用3200余次;2014-2018连续5年进入Elesevier发布的中国高被引学者榜单,2018年首次进入科睿唯安(Clarivate Analytics)发布“高被引科学家”名单。先后主持完成5项国家自然科学基金上面项目和教育部优秀青年教师资助计划等6项省部级科研项目。2010年获湖南省自然科学一等奖(第1完成人);2013年获湖南省教学成果一等奖(第3完成人)。 现担任杂志Advance in Nonlinear Analysis和Advance in Differential Equations的编委。 教育经历 [1] 湖南大学 | 应用数学 | 博士学位 | 博士研究生毕业 [2] 南开大学 | 基础数学 | 硕士学位 | 硕士研究生毕业 [3] 衡阳师专 | 物理 | 无学位 | 大学专科毕业 工作经历 [1] 1995.8-至今 中南大学 | 数学与统计学院 科研项目 [1]具变分结构的几类数学物理方程驻波解动力学性态研究的非经典方法,52万,2020年-2023 年,主持,11971485. [2]几类数学物理方程驻波解的存在性与动力学分析,45万,2016年-2019 年,主持,11571370. [3]强不定非线性Hamilton系统的同宿轨、异宿轨及稳定性, 博士点基金,12万,2013年-2016 年,主持,20120162110021. [4]Hamiltont系统的同宿、异宿轨及相关问题,国家自然科学基金,50万,2012年-2015 年,主持,11171351. [5]时滞微分方程最小周期解及其相关问题研究,国家自然科学基金,27万,2008年-2010 年, 主持. [6]时滞反应扩散方程动力性态的研究,国家自然科学基金,21万,2005年-2007 年,主持. [7]时滞反应扩散方程生态数学模型动力性态的研究,教育部优秀青年教师资助计划项目, 6万,2004年-2005年, 主持. [8]种群生态数学模型动力性态的研究, 回国留学基金,2.0万, 2004年-2005年, 主持. [9]非线性泛函微分方程解的整体性态的研究, 湖南省优秀博士论文基金, 3.0万, 2004年- 2005年,独立. [10]时滞反应扩散方程几类问题研究, 1.5万,湖南省自然科学基金, 2004年-2005年,主持.,完成 获奖信息 [1]Clarivate Analytics “Highly Cited Researchers" in 2018 [2]Most Highly Cited Chinese Researchers ( Elsevier ) from 2014 to 2018 [3]2013年获湖南省教学成果一等奖(第三完成人) [4]2012年获批享受国务院政府特殊津贴 [5]2010年获湖南省自然科学一等奖(第一完成人) [6]2003年获教育部优秀青年教师资助计划项目 [7]湖南省2002年优秀博士论文 期刊编委 [1]期刊 Advance in Nonlinear Analysis 的编委|2019-10-17 [2]期刊 Advance in Differential Equations 的编委|2019-10-17 开设课程 [1]极小极大原理 [2]临界点理论 [3]差分方程 [4]泛函微分方程 [5]线性算子谱理论 [6]矩阵分析 [7]复变函数

研究领域

[1]  非线性偏微分方程、泛函微分方程理论及应用、差分方程理论及应用、Hamilton系统.

非线性偏微分方程; 泛函微分方程理论及应用; 差分方程理论及应用; Hamilton系统。

近期论文

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[1]陈思彤, Alessio Fiscella, Patrizia Pucci, 唐先华.Semiclassical ground state solutions for critical Schrodinger-Poisson systems with lower perturbations.[J]:Journal of Differential Equations [2]陈思彤,唐先华.On the planar Schrodinger-Poisson system with the axially symmetric potential.[J]:Journal of Differential Equations,2019 [3]陈思彤,唐先华,袁帅.Normalized solutions for Schroclinger-Poisson equations with general nonlinearities.[J]:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2020,481(1) [4]顾光泽,唐先华,张友培.Existence of positive solutions for a class of critical fractional Schrodinger-Poisson system with potential vanishing at infinity.[J]:APPLIED MATHEMATICS LETTERS,2020,99 [5]郭挺,唐先华.Ground state solutions of Pohozaev type for the Choquard equation with external Coulomb potential and critical exponent.[J]:APPLIED MATHEMATICS LETTERS,2020,99 [6]陈志,唐先华,张健.Sign-changing multi-bump solutions for the Chern-Simons-Schrodinger equations in R-2.[J]:ADVANCES IN NONLINEAR ANALYSIS,2020,9(1):1066-1091 [7]陈思彤,唐先华.Berestycki-Lions conditions on ground state solutions for a Nonlinear Schrodinger equation with variable potentials.[J]:ADVANCES IN NONLINEAR ANALYSIS,2020,9(1):496-515 [8]唐先华,陈思彤.Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions.[J]:ADVANCES IN NONLINEAR ANALYSIS,2020,9(1):413-437 [9]陈思彤,张彬林,唐先华.Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity.[J]:ADVANCES IN NONLINEAR ANALYSIS,2020,9(1):148-167 [10]林晓燕,唐先华.SOLUTIONS OF NONLINEAR PERIODIC DIRAC EQUATIONS WITH PERIODIC POTENTIALS.[J]:DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S,2019,12(7):2051-2061 [11]顾光泽,唐先华,张友培.GROUND STATES FOR ASYMPTOTICALLY PERIODIC FRACTIONAL KIRCHHOFF EQUATION WITH CRITICAL SOBOLEV EXPONENT.[J]:COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2019,18(6):3181-3200 [12]张友培,唐先华,张健.Existence andmultiplicity of solutions for Kirchhoff type equations involving fractional p-Laplacian without compact condition.[J]:REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FI,2019,113(4):3147-3167 [13]陈思彤,史俊平,唐先华.GROUND STATE SOLUTIONS OF NEHARI-POHOZAEV TYPE FOR THE PLANAR SCHRODINGER-POISSON SYSTEM WITH GENERAL NONLINEARITY.[J]:DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2019,39(10):5867-5889 [14]陈志,唐先华,张宁.STANDING WAVES FOR SCHRODINGER-POISSON SYSTEM WITH GENERAL NONLINEARITY.[J]:DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2019,39(10):6103-6129 [15]张宁,唐先华,陈志.Ground state solutions for the Chern-Simons-Schrodinger equations with general nonlinearity.[J]:COMPLEX VARIABLES AND ELLIPTIC EQUATIONS,2019 [16]陈思彤,唐先华.EXISTENCE OF GROUND STATE SOLUTIONS FOR THE PLANAR AXIALLY SYMMETRIC SCHRODINGER-POISSON SYSTEM.[J]:DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2019,24(9):4685-4702 [17]张亮,唐先华,陈毅.Infinitely Many Solutions for Sublinear Modified Nonlinear Schrodinger Equations Perturbed from Symmetry.[J]:TAIWANESE JOURNAL OF MATHEMATICS,2019,23(4):857-882 [18]陈思彤,张彬林,唐先华.Existence and concentration of semiclassical ground state solutions for the generalized Chern-Simons-Schrodinger system in H-1 (R-2).[J]:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2019,185:68-96 [19]高足,唐先华,陈思彤.Ground state solutions of fractional Choquard equations with general potentials and nonlinearities.[J]:REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FI,2019,113(2):2037-2057 [20]程毕陶,李国发,唐先华.Nehari-type ground state solutions for Kirchhoff type problems in R-N.[J]:APPLICABLE ANALYSIS,2019,98(7):1255-1266 [21]陈思彤,彭嘉伍,唐先华.Radial ground state sign-changing solutions for asymptotically cubic or super-cubic fractional Schrodinger-Poisson systems.[J]:COMPLEX VARIABLES AND ELLIPTIC EQUATIONS,2019 [22]陈志,唐先华,覃蕾.Improved results for Klein-Gorden-Maxwell systems with critical growth.[J]:APPLIED MATHEMATICS LETTERS,2019,91:158-164 [23]秦栋栋,唐先华,吴庆芳.GROUND STATES OF NONLINEAR SCHRODINGER SYSTEMS WITH PERIODIC OR NON-PERIODIC POTENTIALS.[J]:COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2019,18(3):1261-1280 [24]林晓燕,何郁波,唐先华.EXISTENCE AND ASYMPTOTIC BEHAVIOR OF GROUND STATE SOLUTIONS FOR ASYMPTOTICALLY LINEAR SCHRODINGER EQUATION WITH INVERSE SQUARE POTENTIAL.[J]:COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2019,18(3):1547-1565 [25]陈思彤,唐先华.Ground state solutions of Schrodinger-Poisson systems with variable potential and convolution nonlinearity.[J]:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2019,473(1):87-111 [26]彭嘉伍,陈思彤,唐先华.Semiclassical solutions for linearly coupled Schrodinger equations without compactness.[J]:COMPLEX VARIABLES AND ELLIPTIC EQUATIONS,2019,64(4):548-556 [27]张友培,唐先华,张健.Existence of infinitely many solutions for fractional p-Laplacian Schrodinger-Kirchhoff type equations with sign-changing potential.[J]:REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FI,2019,113(2):569-586 [28]陈思彤,唐先华.Radial ground state sign-changing solutions for a class of asymptotically cubic or super-cubic Schrodinger-Poisson type problems.[J]:REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FI,2019,113(2):627-643 [29]陈思彤,唐先华.Geometrically distinct solutions for Klein-Gordon-Maxwell systems with super-linear nonlinearities.[J]:APPLIED MATHEMATICS LETTERS,2019,90:188-193 [30]陈毅,唐先华.Nehari-type ground state solutions for Schrodinger equations with Hardy potential and critical nonlinearities.[J]:COMPLEX VARIABLES AND ELLIPTIC EQUATIONS,2019 [31]唐先华,林晓燕,庾建设.Nontrivial Solutions for Schrodinger Equation with Local Super-Quadratic Conditions.[J]:JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,2019,31(1):369-383 [32]陈思彤,唐先华,庾建设.Sign-changing ground state solutions for discrete nonlinear Schrodinger equations.[J]:JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS,2019,25(2):202-218 [33]陈建华,唐先华,程毕陶.35.EXISTENCE OF GROUND STATE SOLUTIONS FOR A CLASS OF QUASILINEAR SCHRODINGER EQUATIONS WITH GENERAL CRITICAL NONLINEARITY.[J]:COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2019,18(1):493-517 [34]高足,唐先华,陈思彤.On existence and concentration behavior of positive ground state solutions for a class of fractional Schrodinger-Choquard equations.[J]:ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK,2018,69(5) [35]陈思彤,唐先华,廖芳芳.Existence and asymptotic behavior of sign-changing solutions for fractional Kirchhoff-type problems in low dimensions.[J]:NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICA,2018,25(5) [36]陈思彤,唐先华.Ground state solutions for generalized quasilinear Schrodinger equations with variable potentials and Berestycki-Lions nonlinearities.[J]:JOURNAL OF MATHEMATICAL PHYSICS,2018,59(8) [37]高足,唐先华,陈思彤.On the Existence of Ground State Solutions for Fractional Schrodinger-Poisson Systems with General Potentials and Super-quadratic Nonlinearity.[J]:MEDITERRANEAN JOURNAL OF MATHEMATICS,2018,15(3) [38]秦栋栋,何郁波,唐先华.Ground State and Multiple Solutions for Kirchhoff Type Equations With Critical Exponent.[J]:CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN D,2018,61(2):353-369 [39]罗虎啸,唐先华,高足.SIGN-CHANGING SOLUTIONS FOR NON-LOCAL ELLIPTIC EQUATIONS WITH ASYMPTOTICALLY LINEAR TERM.[J]:COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2018,17(3):1147-1159 [40]陈思彤,唐先华.IMPROVED RESULTS FOR KLEIN-GORDON-MAXWELL SYSTEMS WITH GENERAL NONLINEARITY.[J]:DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2018,38(5):2333-2348 [41]陈建华,唐先华,程毕陶.Existence of ground state solutions for quasilinear Schrodinger equations with super-quadratic condition.[J]:APPLIED MATHEMATICS LETTERS,2018,79:27-33 [42]罗虎啸,唐先华.Ground state and multiple solutions for the fractional Schrodinger-Poisson system with critical Sobolev exponent.[J]:NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,2018,42:24-52 [43]陈思彤,唐先华.Infinitely many solutions and least energy solutions for Klein-Gordon-Maxwell systems with general superlinear nonlinearity.[J]:COMPUTERS & MATHEMATICS WITH APPLICATIONS,2018,75(9):3358-3366 [44]张健,张文,唐先华.Semiclassical limits of ground states for Hamiltonian elliptic system with gradient term.[J]:NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,2018,40:377-402 [45]罗虎啸,唐先华,高足.Ground state sign-changing solutions for fractional Kirchhoff equations in bounded domains.[J]:JOURNAL OF MATHEMATICAL PHYSICS,2018,59(3) [46]陈建华,唐先华,程毕陶.Existence and nonexistence of positive solutions for a class of generalized quasilinear Schrodinger equations involving a Kirchhoff-type perturbation with critical Sobolev exponent.[J]:JOURNAL OF MATHEMATICAL PHYSICS,2018,59(2) [47]高足,唐先华,陈思彤.Existence of ground state solutions of Nehari-Pohozaev type for fractional Schrodinger-Poisson systems with a general potential.[J]:COMPUTERS & MATHEMATICS WITH APPLICATIONS,2018,75(2):614-631 [48]秦栋栋,唐先华.Time-harmonic and asymptotically linear Maxwell equations in anisotropic media.[J]:MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2018,41(1):317-335 [49]陈建华,程毕陶,唐先华.New existence of multiple solutions for nonhomogeneous Schrodinger-Kirchhoff problems involving the fractional p-Laplacian with sign-changing potential.[J]:REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FI,2018,112(1):153-176 [50]陈建华,唐先华,程毕陶.Non-Nehari manifold method for a class of generalized quasilinear Schrodinger equations.[J]:APPLIED MATHEMATICS LETTERS,2017,74:20-26 [51]张文,唐先华,张健.MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR FOURTH-ORDER ELLIPTIC EQUATIONS WITH MIXED NONLINEARITY.[J]:ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS,2017 [52]陈建华,唐先华,高足.Existence of ground state sign-changing solutions for p-Laplacian equations of Kirchhoff type.[J]:MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2017,40(14):5056-5067 [53]陈思彤,彭嘉伍,唐先华.Ground state solutions for asymptotically periodic fractional Schrodinger-Poisson problems with asymptotically cubic or super-cubic nonlinearities.[J]:MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2017,40(13):4948-4961 [54]陈思彤,唐先华.Ground state sign-changing solutions for asymptotically cubic or super-cubic Schrodinger-Poisson systems without compact condition.[J]:COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,74(3):446-458 [55]陈建华,唐先华,程毕陶.Existence of ground state sign-changing solutions for a class of generalized quasilinear Schrodinger-Maxwell system in R-3.[J]:COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,74(3):466-481 [56]唐先华,陈思彤.Ground state solutions of Nehari-Pohozaev type for Kirchhoff-type problems with general potentials.[J]:CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQ,2017,56(4) [57]陈思彤,唐先华.Infinitely many solutions for super-quadratic Kirchhoff-type equations with sign-changing potential.[J]:APPLIED MATHEMATICS LETTERS,2017,67:40-45 [58]张亮,唐先华,陈毅.INFINITELY MANY SOLUTIONS FOR A CLASS OF PERTURBED ELLIPTIC EQUATIONS WITH NONLOCAL OPERATORS.[J]:COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2017,16(3):823-842 [59]张亮,唐先华,陈毅.Infinitely many solutions for indefinite quasilinear Schrodinger equations under broken symmetry situations.[J]:MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2017,40(4):979-991 [60]唐先华,张健.Ground state solutions of Nehari-Pankov type for a superlinear elliptic system on RN.[J]:MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2017,40(3):729-740 [61]罗虎啸,李胜军,唐先华.Nontrivial Solution for the Fractional p-Laplacian Equations via Perturbation Methods.[J]:ADVANCES IN MATHEMATICAL PHYSICS,2017 [62]程毕陶,唐先华.High energy solutions of modified quasilinear fourth-order elliptic equations with sign-changing potential.[J]:COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,73(1):27-36 [63]陈建华,唐先华,高足.Existence of multiple solutions for modified Schrodinger-Kirchhoff-Poisson type systems via perturbation method with sign-changing potential.[J]:COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,73(3):505-519 [64]陈思彤,李印彬,唐先华.SIGN-CHANGING SOLUTIONS FOR ASYMPTOTICALLY LINEAR SCHRODINGER EQUATION IN BOUNDED DOMAINS.[J]:ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS,2016 [65]程毕陶,唐先华.New Existence of Solutions for the Fractional p-Laplacian Equations with Sign-Changing Potential and Nonlinearity.[J]:MEDITERRANEAN JOURNAL OF MATHEMATICS,2016,13(5):3373-3387 [66]黄文念,唐先华.Ground-State Solutions for Asymptotically Cubic Schrodinger-Maxwell Equations.[J]:MEDITERRANEAN JOURNAL OF MATHEMATICS,2016,13(5):3469-3481 [67]高足,唐先华,张文.LEAST ENERGY SIGN-CHANGING SOLUTIONS FOR NONLINEAR PROBLEMS INVOLVING FRACTIONAL LAPLACIAN.[J]:ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS,2016 [68]唐先华,程毕陶.Ground state sign-changing solutions for Kirchhoff type problems in bounded domains.[J]:JOURNAL OF DIFFERENTIAL EQUATIONS,2016,261(4):2384-2402 [69]张文,唐先华,张健.Existence and concentration of solutions for Schrodinger-Poisson system with steep potential well.[J]:MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2016,39(10):2549-2557 [70]唐先华.Non-Nehari Manifold Method for Periodic Discrete Superlinear Schrodinger Equation.[J]:ACTA MATHEMATICA SINICA-ENGLISH SERIES,2016,32(4):463-473 [71]唐先华,陈思彤.WEAK POTENTIAL CONDITIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL NONLINEARITIES.[J]:JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY,2016,100(2):272-288 [72]陈鹏,何小飞,唐先华.Infinitely many solutions for a class of fractional Hamiltonian systems via critical point theory.[J]:MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2016,39(5):1005-1019 [73]秦栋栋,何郁波,唐先华.Ground state solutions for Kirchhoff type equations with asymptotically 4-linear nonlinearity.[J]:COMPUTERS & MATHEMATICS WITH APPLICATIONS,2016,71(7):1524-1536 [74]唐先华,秦栋栋.Ground state solutions for semilinear time-harmonic Maxwell equations.[J]:JOURNAL OF MATHEMATICAL PHYSICS,2016,57(4) [75]张文,唐先华,张健.Stationary solutions for a superlinear Dirac equation.[J]:MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2016,39(4):796-805 [76]何郁波,唐先华.Numerical simulations of a family of the coupled viscous Burgers, equation using the lattice Boltzmann method.[J]:JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERI,2016 [77]张亮,唐先华,陈毅.Infinitely many solutions for a class of indefinite biharmonic equation under symmetry breaking situations.[J]:COMPLEX VARIABLES AND ELLIPTIC EQUATIONS,2016,61(9):1334-1352 [78]唐先华.Infinitely many homoclinic solutions for a second-order Hamiltonian system.[J]:MATHEMATISCHE NACHRICHTEN,2016,289(1):116-127 [79]张健,唐先华,张文.Ground states for diffusion system with periodic and asymptotically periodic nonlinearity.[J]:COMPUTERS & MATHEMATICS WITH APPLICATIONS,2016,71(2):633-641 [80]张健,唐先华,张文.GROUND STATE SOLUTIONS FOR A CLASS OF NONLINEAR MAXWELL-DIRAC SYSTEM.[J]:TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS,2015,46(2):785-798 [81]张健,唐先华,张文.Existence and multiplicity of stationary solutions for a class of Maxwell-Dirac system.[J]:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2015,127:298-311 [82]廖芳芳,唐先华,秦栋栋.NEW CONDITIONS ON GROUND STATE SOLUTIONS FOR HAMILTONIAN ELLIPTIC SYSTEMS WITH GRADIENT TERMS.[J]:BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY,2015,41(5):1131-1146 [83]秦栋栋,唐先华.NEW CONDITIONS ON SOLUTIONS FOR PERIODIC SCHRODINGER EQUATIONS WITH SPECTRUM ZERO.[J]:TAIWANESE JOURNAL OF MATHEMATICS,2015,19(4):977-993 [84]秦栋栋,唐先华.TWO TYPES OF GROUND STATE SOLUTIONS FOR A PERIODIC SCHRODINGER EQUATIONS WITH ZERO ON THE BOUNDARY OF THE SPECTRUM.[J]:ELECTRONIC JOURNAL 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