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Number of synchronized and segregated interior spike solutions for nonlinear coupled elliptic systems with continuous potentials

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Science China Mathematics 2019年第3期62卷 509-534页

作者： Lushun Wang School of Mathematical Sciences Beijing Normal University

In this paper, we consider the following nonlinear coupled elliptic systems with continuous potentials:{-ε~2?u +(1 + δP(x))u = μ1 u^3+ βuv^2 in ?,-ε~2?v +(1 + δQ(x))v = μ2 v^3+ βu^2 v in ?,u > 0, v > 0 in ?,(?u)/(?v)=(?ν)/(?ν)=0on ??,(A_ε)where ? is a smooth bounded domain in R^N for N = 2, 3, δ, ε, μ_1 and μ_2 are positive parameters, β∈ R,P(x) and Q(x) are two smooth potentials defined on ?, the closure of ?. Due to Liapunov-Schmidt reduction method, we prove that(A_ε) has at least O(1/(ε| ln ε|)~N) synchronized and O(1/(ε| ln ε|)^(2 N)) segregated vector solutions for ε and δ small enough and some β∈ R. Moreover, for each m ∈(0, N) there exist synchronized and segregated vector solutions for(A_ε) with energies in the order of ε^(N-m). Our results extend the result of Lin et al.(2007) from the Lin-Ni-Takagi problem to the nonlinear Schr¨odinger elliptic systems with continuous potentials.

关键词： nonlinear coupled elliptic system Liapunov-Schmidt reduction methods synchronized and segregated vector solutions

RADIAL CONVEX solutions OF A SINGULAR DIRICHLET PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE

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Acta Mathematica Scientia 2019年第2期39卷 395-402页

作者：梁载涛杨艳娟 School of Mathematics and Big Data Anhui University of Science and Technology College of Sciences Hohai University

In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theo... 详细信息

关键词： radial convex solutions singular Dirichlet problem mean curvature operator fixed point theorem in cones

New Optical Soliton solutions of the Perturbed Fokas-Lenells Equation

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Communications in Theoretical Physics 2019年第11期71卷 1275-1280页

作者： Maha S.M.Shehata Hadi Rezazadeh Emad H.M.Zahran Eric Tala-Tebue Ahmet Bekir Departments of Mathematics Zagazig UniversityFaculty of ScienceZagazigEgypt Faculty of Engineering Technology Amol University of Special Modern TechnologiesAmolIran Departments of Mathematical and Physical Engineering Benha UniversityFaculty of EngineeringShubraEgypt Laboratoire D'Automatique et D'Informatique Appliquee(LAIA) IUT-FV of BandjounThe University of DschangBP 134BandjounCameroon Neighbourhood of Akcaglan Imarli StreetNumber:28/426030EskisehirTurkey

In this article, we employ the perturbed Fokas-Lenells equation(FLE), which represents recent electronic communications. The Riccati-Bernoulli Sub-ODE method which does not depend on the balance rule is used for thefirst time to obtain the new exact and solitary wave solutions of this equation. This technique is direct, effective and reduces the large volume of calculations.

关键词： perturbed Fokas-Lenells equation(FLE) Riccati-Bernoulli Sub-ODE method optical soliton solutions

Multiple Periodic solutions of Differential Delay Equations with 2k-1 Lags

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Acta Mathematicae Applicatae Sinica 2020年第2期36卷 390-400页

作者： Lin LI Hua-fei SUN Wei-gao GE School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

In this paper,we study the periodic solutions to a type of differential delay equations with 2 k-1 lags.The 4 k-periodic solutions are obtained by using the variational method and the method of Kaplan-Yorke coupling system.This is a new type of differential delay equations compared with all the previous researches.And this paper provides a theoretical basis for the study of differential delay equations.An example is given to demonstrate our main results.

关键词： differential delay equation periodic solutions critical point theory variational method

Existence of almost periodic solutions of neutral differential equations with piecewise constant argument

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Science China Mathematics 1996年第11期39卷 1164-1177页

作者：袁荣洪佳林 Department of Mathematics Beijing Normal University Beijing 100875 China Institute of Applied Mathematics Chinese Academy of Sciences Beijing 100080 China

Based on the properties on almost periodic sequence, it is proved that the almost periodic solutions for a class of neutral differential equations with piecewise constant argument exist.

关键词： almost periodic solutions almost periodic sequences piecewise constant argument neutral differential equations.

Valence electron structure of the(ZrTi)B_2 solid solutions calculated by the three models

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Science China(Technological Sciences) 2009年第5期52卷 1195-1201页

作者： LI JinPing,HAN JieCai,MENG SongHe & WANG BaoLin Center for Composite Materials,Harbin Institute of Technology,Harbin150001,China Center for Composite Materials Harbin Institute of Technology Harbin China

The Zr-rich(Zr0.8Ti0.2)B2 and the Ti-rich(Ti0.8Zr0.2)B2 solid solutions are formed when TiB2 and ZrB2 are hot-pressed.To forecast the properties of the two solid solutions,their valence electron structure was analyzed based on the empirical electron theory(EET) of solids and molecules.We used three different models,the average atom model,the average cell model and the real cell model,and compared with the calculation results from the three models.In the real cell model,the lattice constants of the solid solu-tions were supposed to be changed or unchanged.The results showed that different models could only result in slight change in the hybridization levels of the metal atoms in the two solid solutions and little difference between the calculation values.However,they can not change the variant trend of the va-lence electron structure nor the properties of the solid solutions.Thus,the three models and the methods are appropriate and the calculation results are reasonable and consistent.

关键词： (ZrTi)B2 solid solutions empirical electron theory the calculation models

High-Order Lump-Type solutions and Their Interaction solutions to a (3+1)-Dimensional Nonlinear Evolution Equation

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Communications in Theoretical Physics 2019年第8期71卷 927-934页

作者：方涛王惠王云虎马文秀 College of Art and Sciences Shanghai Maritime University Shanghai 201306 China Department of Mathematics and Statistics University of South Florida Tampa FL 33620 USA Department of Mathematics and Information Technology The Education University of Hong Kong Hong Kong China Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia College of Mathematics and System Science Shandong University of Science and Technology Qingdao 266590 China Department of Mathematical Sciences North-West University Mafikeng Campus Mmabatho 2735 South Africa

By means of the Hirota bilinear method and symbolic computation, high-order lump-type solutions and a kind of interaction solutions are presented for a(3+1)-dimensional nonlinear evolution equation.The high-order lumptype solutions of the associated Hirota bilinear equation are presented, which is a kind of positive quartic-quadraticfunction solution.At the same time, the interaction solutions can also be obtained, which are linear combination solutions of quartic-quadratic-functions and hyperbolic cosine functions.Physical properties and dynamical structures of two classes of the presented solutions are demonstrated in detail by their graphs.

关键词： high-order lump-type solutions interaction solutions Hirota bilinear method

Wave packet solutions in a bounded equatorial ocean and its interannual and decadal variabilities

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Acta Oceanologica Sinica 2019年第3期38卷 45-59页

作者： Dongling Zhang Juan Zhu Xu Lu Ming Zhang Institute of Atmospheric Physics Chinese Academy of Sciences Special Office of Marine Environment National Marine Environment Forecasting Center Ministry of Natural Resources Atmospheric Circulation and Short-term Climate Prediction Laboratory of Meteorology and Marine Institute National University of Defense Technology 32021 Troop People's Liberation Army

Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results are as follows. The wave packet is a superposition of eastward travelling Kelvin waves and westward travelling Rossby waves with the slowest speed, and satisfies the boundary conditions of eastern and western coasts, respectively.The decay coefficient of this solution to the north and south sides of the equator is inversely proportional only to the phase velocity of Kelvin waves in the upper water. The oscillation frequency of the wave packet, which is also the natural frequency of the ocean, is proportional to its mode number and the phase velocity of Kelvin waves and is inversely proportional to the length of the equatorial ocean in the east-west direction. The flow anomalies of the wave packet of Mode 1 most of the time appear as zonal flows with the same direction. They reach the maximum at the center of the equatorial ocean and decay rapidly away from the equator, manifested as equatorially trapped waves. The flow anomalies of the wave packet of Mode 2 appear as the zonal flows with the same direction most of the time in half of the ocean, and are always 0 at the center of the entire ocean which indicates stagnation, while decaying away from the equator with the same speed as that of Mode 1. The spatial structure and oscillation period of the wave packet solution of Mode 1 and Mode 2 are consistent with the changing periods of the surface spatial field and time coefficient of the first and second modes of complex empirical orthogonal function(EOF)analysis of flow anomalies in the actual equatorial ocean. This indicates that the solution does exist in the real ocean, and that El Ni?o-Southern Oscillation(ENSO) and Indian Ocean dipole(IOD) are both related to Mode 2.After considering the Indonesian throughflow, we can obtain the length of bounded equatorial ocean by taking the sum of that of the tr

关键词： bounded equatorial ocean wave packet solutions decadal variability Kelvin wave Rossby wave

GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL solutions TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL

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Acta Mathematica Scientia 2019年第6期39卷 1525-1537页

作者：丁时进黄丙远黎泉荣 South China Research Center for Applied Mathematics and Interdisciplinary Studies School of Mathematical SciencesSouth China Normal UniversityGuangzhou 510631China School of Mathematics and Statistics Hanshan Normal UniversityChaozhou 521041China College of Mathematics and Statistics Shenzhen UniversityShenzhen 518060China

We prove the global existence of classical solutions to a fluid-particle interaction model in R^3, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state(ρ*, 0, η*) and the external potential satisfies the smallness assumption. Furthermore, optimal decay rates of classical solutions in H^3-framework are obtained.

关键词： compressible Navier-Stokes-Smoluchowski global classical solutions optimal decay rates