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AIMS joins the mathematics community world wide in congratulating Professor Alessio Figalli on being awarded the Fields Medal 2018. Professor Figallihas made important contributions to AIMS journals and conferences. Heserved as the Managing Editor of Discrete and Continuous Dynamical Systemsfrom 2012 to 2016 and delivered a plenary lecture at the 11th AIMS conference (2016) in Orlando, USA. Details can be found at  http://aimsciences.org/conferences/2016/2016_speakers.html

Congratulations, Alessio!


DCDS, series A includes peer-reviewed original papers and invited expository papers on the theory and methods of analysis, differential equations and dynamical systems. This journal is committed to recording important new results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.

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Preface: DCDS-A special issue to honor Wei-Ming Ni's 70th birthday
Chiun-Chuan Chen, Yuan Lou, Hirokazu Ninomiya, Peter Polacik and Xuefeng Wang
2020, 40(6) : ⅰ-ⅱ doi: 10.3934/dcds.2020171 +[Abstract](479) +[HTML](191) +[PDF](78.36KB)
Bifurcation from infinity with applications to reaction-diffusion systems
Chihiro Aida, Chao-Nien Chen, Kousuke Kuto and Hirokazu Ninomiya
2020, 40(6) : 3031-3055 doi: 10.3934/dcds.2020053 +[Abstract](532) +[HTML](185) +[PDF](380.03KB)
Evolution equations involving nonlinear truncated Laplacian operators
Matthieu Alfaro and Isabeau Birindelli
2020, 40(6) : 3057-3073 doi: 10.3934/dcds.2020046 +[Abstract](434) +[HTML](205) +[PDF](378.54KB)
Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small
Xueli Bai and Fang Li
2020, 40(6) : 3075-3092 doi: 10.3934/dcds.2020035 +[Abstract](492) +[HTML](209) +[PDF](384.66KB)
Mean field equations on tori: Existence and uniqueness of evenly symmetric blow-up solutions
Daniele Bartolucci, Changfeng Gui, Yeyao Hu, Aleks Jevnikar and Wen Yang
2020, 40(6) : 3093-3116 doi: 10.3934/dcds.2020039 +[Abstract](451) +[HTML](184) +[PDF](475.57KB)
A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic fisher kpp equation
Michiel Bertsch, Danielle Hilhorst, Hirofumi Izuhara, Masayasu Mimura and Tohru Wakasa
2020, 40(6) : 3117-3142 doi: 10.3934/dcds.2019226 +[Abstract](1362) +[HTML](443) +[PDF](496.79KB)
Signed Radon measure-valued solutions of flux saturated scalar conservation laws
Michiel Bertsch, Flavia Smarrazzo, Andrea Terracina and Alberto Tesei
2020, 40(6) : 3143-3169 doi: 10.3934/dcds.2020041 +[Abstract](341) +[HTML](169) +[PDF](496.87KB)
On the spectral theory of positive operators and PDE applications
Kung-Ching Chang, Xuefeng Wang and Xie Wu
2020, 40(6) : 3171-3200 doi: 10.3934/dcds.2020054 +[Abstract](520) +[HTML](221) +[PDF](460.48KB)
On gaussian curvature equation in $ \mathbb{R}^2 $ with prescribed nonpositive curvature
Huyuan Chen, Dong Ye and Feng Zhou
2020, 40(6) : 3201-3214 doi: 10.3934/dcds.2020125 +[Abstract](157) +[HTML](99) +[PDF](365.89KB)
Nondegeneracy of harmonic maps from $ {{\mathbb{R}}^{2}} $ to $ {{\mathbb{S}}^{2}} $
Guoyuan Chen, Yong Liu and Juncheng Wei
2020, 40(6) : 3215-3233 doi: 10.3934/dcds.2019228 +[Abstract](960) +[HTML](386) +[PDF](387.83KB)
A Hopf lemma and regularity for fractional $ p $-Laplacians
Wenxiong Chen, Congming Li and Shijie Qi
2020, 40(6) : 3235-3252 doi: 10.3934/dcds.2020034 +[Abstract](379) +[HTML](178) +[PDF](403.05KB)
Boundary spike of the singular limit of an energy minimizing problem
Xinfu Chen, Huiqiang Jiang and Guoqing Liu
2020, 40(6) : 3253-3290 doi: 10.3934/dcds.2020124 +[Abstract](156) +[HTML](102) +[PDF](461.47KB)
On the family of non-topological solutions for the elliptic system arising from a product Abelian gauge field theory
Jann-Long Chern, Sze-Guang Yang, Zhi-You Chen and Chih-Her Chen
2020, 40(6) : 3291-3304 doi: 10.3934/dcds.2020127 +[Abstract](146) +[HTML](99) +[PDF](382.66KB)
Sectional symmetry of solutions of elliptic systems in cylindrical domains
Lucio Damascelli and Filomena Pacella
2020, 40(6) : 3305-3325 doi: 10.3934/dcds.2020045 +[Abstract](338) +[HTML](154) +[PDF](418.61KB)
Type Ⅱ finite time blow-up for the energy critical heat equation in $ \mathbb{R}^4 $
Manuel del Pino, Monica Musso, Juncheng Wei and Yifu Zhou
2020, 40(6) : 3327-3355 doi: 10.3934/dcds.2020052 +[Abstract](487) +[HTML](214) +[PDF](494.08KB)
Spike solutions for a mass conservation reaction-diffusion system
Shin-Ichiro Ei and Shyuh-Yaur Tzeng
2020, 40(6) : 3357-3374 doi: 10.3934/dcds.2020049 +[Abstract](387) +[HTML](183) +[PDF](372.45KB)
Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity
Maho Endo, Yuki Kaneko and Yoshio Yamada
2020, 40(6) : 3375-3394 doi: 10.3934/dcds.2020033 +[Abstract](519) +[HTML](203) +[PDF](208.91KB)
Large time behavior of ODE type solutions to nonlinear diffusion equations
Junyong Eom and Kazuhiro Ishige
2020, 40(6) : 3395-3409 doi: 10.3934/dcds.2019229 +[Abstract](1057) +[HTML](373) +[PDF](363.45KB)
Asymptotic population abundance of a two-patch system with asymmetric diffusion
Mengting Fang, Yuanshi Wang, Mingshu Chen and Donald L. DeAngelis
2020, 40(6) : 3411-3425 doi: 10.3934/dcds.2020031 +[Abstract](358) +[HTML](212) +[PDF](622.93KB)
On the viscous Camassa-Holm equations with fractional diffusion
Zaihui Gan, Fanghua Lin and Jiajun Tong
2020, 40(6) : 3427-3450 doi: 10.3934/dcds.2020029 +[Abstract](438) +[HTML](173) +[PDF](414.4KB)
The sign of traveling wave speed in bistable dynamics
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara and Chang-Hong Wu
2020, 40(6) : 3451-3466 doi: 10.3934/dcds.2020047 +[Abstract](526) +[HTML](207) +[PDF](332.61KB)
A stage structured model of delay differential equations for Aedes mosquito population suppression
Mugen Huang, Moxun Tang, Jianshe Yu and Bo Zheng
2020, 40(6) : 3467-3484 doi: 10.3934/dcds.2020042 +[Abstract](429) +[HTML](286) +[PDF](515.07KB)
Cauchy problem of semilinear inhomogeneous elliptic equations of Matukuma-type with multiple growth terms
Yunfeng Jia, Yi Li, Jianhua Wu and Hong-Kun Xu
2020, 40(6) : 3485-3507 doi: 10.3934/dcds.2019227 +[Abstract](995) +[HTML](436) +[PDF](416.37KB)
Global stabilization of the full attraction-repulsion Keller-Segel system
Hai-Yang Jin and Zhi-An Wang
2020, 40(6) : 3509-3527 doi: 10.3934/dcds.2020027 +[Abstract](378) +[HTML](180) +[PDF](396.76KB)
Eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a large zonal domain in the unit sphere
Yoshitsugu Kabeya
2020, 40(6) : 3529-3559 doi: 10.3934/dcds.2020040 +[Abstract](336) +[HTML](160) +[PDF](387.07KB)
On the limiting system in the Shigesada, Kawasaki and Teramoto model with large cross-diffusion rates
Yukio Kan-On
2020, 40(6) : 3561-3570 doi: 10.3934/dcds.2020161 +[Abstract](134) +[HTML](86) +[PDF](1908.79KB)
Asymmetric dispersal and evolutional selection in two-patch system
Yong-Jung Kim, Hyowon Seo and Changwook Yoon
2020, 40(6) : 3571-3593 doi: 10.3934/dcds.2020043 +[Abstract](657) +[HTML](236) +[PDF](745.65KB)
Hysteresis-driven pattern formation in reaction-diffusion-ODE systems
Alexandra Köthe, Anna Marciniak-Czochra and Izumi Takagi
2020, 40(6) : 3595-3627 doi: 10.3934/dcds.2020170 +[Abstract](114) +[HTML](117) +[PDF](1079.38KB)
Spectral asymptotics of radial solutions and nonradial bifurcation for the Hénon equation
Joel Kübler and Tobias Weth
2020, 40(6) : 3629-3656 doi: 10.3934/dcds.2020032 +[Abstract](453) +[HTML](178) +[PDF](484.63KB)
Existence and instability of some nontrivial steady states for the SKT competition model with large cross diffusion
Qing Li and Yaping Wu
2020, 40(6) : 3657-3682 doi: 10.3934/dcds.2020051 +[Abstract](375) +[HTML](160) +[PDF](693.91KB)
Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach
Qian Liu, Shuang Liu and King-Yeung Lam
2020, 40(6) : 3683-3714 doi: 10.3934/dcds.2020050 +[Abstract](351) +[HTML](173) +[PDF](766.32KB)
A functional approach towards eigenvalue problems associated with incompressible flow
Shuang Liu and Yuan Lou
2020, 40(6) : 3715-3736 doi: 10.3934/dcds.2020028 +[Abstract](431) +[HTML](190) +[PDF](453.64KB)
Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature
Tianwen Luo, Tao Tao and Liqun Zhang
2020, 40(6) : 3737-3765 doi: 10.3934/dcds.2019230 +[Abstract](861) +[HTML](375) +[PDF](448.81KB)
Perturbative techniques for the construction of spike-layers
Andrea Malchiodi
2020, 40(6) : 3767-3787 doi: 10.3934/dcds.2020055 +[Abstract](378) +[HTML](225) +[PDF](390.03KB)
Asymptotic homogenization for delay-differential equations and a question of analyticity
John Mallet-Paret and Roger D. Nussbaum
2020, 40(6) : 3789-3812 doi: 10.3934/dcds.2020044 +[Abstract](333) +[HTML](228) +[PDF](402.96KB)
Turing type instability in a diffusion model with mass transport on the boundary
Yoshihisa Morita and Kunimochi Sakamoto
2020, 40(6) : 3813-3836 doi: 10.3934/dcds.2020160 +[Abstract](134) +[HTML](102) +[PDF](355.44KB)
Indefinite nonlinear diffusion problem in population genetics
Kimie Nakashima
2020, 40(6) : 3837-3855 doi: 10.3934/dcds.2020169 +[Abstract](120) +[HTML](45) +[PDF](374.36KB)
A priori estimates and multiplicity for systems of elliptic PDE with natural gradient growth
Gabrielle Nornberg, Delia Schiera and Boyan Sirakov
2020, 40(6) : 3857-3881 doi: 10.3934/dcds.2020128 +[Abstract](199) +[HTML](85) +[PDF](504.48KB)
Convergence and structure theorems for order-preserving dynamical systems with mass conservation
Toshiko Ogiwara, Danielle Hilhorst and Hiroshi Matano
2020, 40(6) : 3883-3907 doi: 10.3934/dcds.2020129 +[Abstract](215) +[HTML](112) +[PDF](407.73KB)
Variational and operator methods for Maxwell-Stokes system
Xing-Bin Pan
2020, 40(6) : 3909-3955 doi: 10.3934/dcds.2020036 +[Abstract](397) +[HTML](231) +[PDF](545.81KB)
The impact of the domain boundary on an inhibitory system: Interior discs and boundary half discs
Xiaofeng Ren and David Shoup
2020, 40(6) : 3957-3979 doi: 10.3934/dcds.2020048 +[Abstract](296) +[HTML](162) +[PDF](603.83KB)
Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations
Masaharu Taniguchi
2020, 40(6) : 3981-3995 doi: 10.3934/dcds.2020126 +[Abstract](138) +[HTML](97) +[PDF](419.08KB)
On space-time periodic solutions of the one-dimensional heat equation
Dong-Ho Tsai and Chia-Hsing Nien
2020, 40(6) : 3997-4017 doi: 10.3934/dcds.2020037 +[Abstract](369) +[HTML](171) +[PDF](444.59KB)
Monotone and nonmonotone clines with partial panmixia across a geographical barrier
Yantao Wang and Linlin Su
2020, 40(6) : 4019-4037 doi: 10.3934/dcds.2020056 +[Abstract](357) +[HTML](215) +[PDF](902.38KB)
Refined regularity and stabilization properties in a degenerate haptotaxis system
Michael Winkler and Christian Stinner
2020, 40(6) : 4039-4058 doi: 10.3934/dcds.2020030 +[Abstract](293) +[HTML](161) +[PDF](401.32KB)
Simulation of post-hurricane impact on invasive species with biological control management
Linhao Xu, Marya Claire Zdechlik, Melissa C. Smith, Min B. Rayamajhi, Don L. DeAngelis and Bo Zhang
2020, 40(6) : 4059-4071 doi: 10.3934/dcds.2020038 +[Abstract](461) +[HTML](223) +[PDF](842.56KB)
Rigidity of random group actions
Woochul Jung, Keonhee Lee, Carlos Morales and Jumi Oh
2020doi: 10.3934/dcds.2020130 +[Abstract](167) +[HTML](105) +[PDF](292.41KB)
Generic Birkhoff spectra
Zoltán Buczolich, Balázs Maga and Ryo Moore
2020doi: 10.3934/dcds.2020131 +[Abstract](174) +[HTML](87) +[PDF](484.2KB)
Maximal equicontinuous generic factors and weak model sets
Gerhard Keller
2020doi: 10.3934/dcds.2020132 +[Abstract](127) +[HTML](79) +[PDF](449.9KB)
The secant map applied to a real polynomial with multiple roots
Antonio Garijo and Xavier Jarque
2020doi: 10.3934/dcds.2020133 +[Abstract](119) +[HTML](78) +[PDF](492.96KB)
On the measure of KAM tori in two degrees of freedom
Luca Biasco and Luigi Chierchia
2020doi: 10.3934/dcds.2020134 +[Abstract](137) +[HTML](87) +[PDF](394.63KB)
Gaussian iterative algorithm and integrated automorphism equation for random means
Justyna Jarczyk and Witold Jarczyk
2020doi: 10.3934/dcds.2020135 +[Abstract](117) +[HTML](87) +[PDF](293.27KB)
Entire and ancient solutions of a supercritical semilinear heat equation
Peter Poláčik and Pavol Quittner
2020doi: 10.3934/dcds.2020136 +[Abstract](161) +[HTML](81) +[PDF](417.52KB)
Time-fractional equations with reaction terms: Fundamental solutions and asymptotics
Serena Dipierro, Benedetta Pellacci, Enrico Valdinoci and Gianmaria Verzini
2020doi: 10.3934/dcds.2020137 +[Abstract](199) +[HTML](93) +[PDF](373.7KB)
Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions
João Marcos do Ó, Bruno Ribeiro and Bernhard Ruf
2020doi: 10.3934/dcds.2020138 +[Abstract](354) +[HTML](90) +[PDF](1397.84KB)
Computer assisted proofs of two-dimensional attracting invariant tori for ODEs
Maciej J. Capiński, Emmanuel Fleurantin and J. D. Mireles James
2020doi: 10.3934/dcds.2020162 +[Abstract](76) +[HTML](43) +[PDF](3490.25KB)
On the regularity of the Green current for semi-extremal endomorphisms of $ \mathbb{P}^2 $
Christophe Dupont and Axel Rogue
2020doi: 10.3934/dcds.2020163 +[Abstract](53) +[HTML](29) +[PDF](359.72KB)
On globally hypoelliptic abelian actions and their existence on homogeneous spaces
Danijela Damjanovic, James Tanis and Zhenqi Jenny Wang
2020doi: 10.3934/dcds.2020164 +[Abstract](63) +[HTML](40) +[PDF](534.48KB)
Euler integral and perihelion librations
Gabriella Pinzari
2020doi: 10.3934/dcds.2020165 +[Abstract](59) +[HTML](36) +[PDF](750.63KB)
A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold
Marian Gidea, Rafael de la Llave and Tere M. Seara
2020doi: 10.3934/dcds.2020166 +[Abstract](70) +[HTML](29) +[PDF](358.85KB)
Mean equicontinuity, complexity and applications
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2020doi: 10.3934/dcds.2020167 +[Abstract](78) +[HTML](45) +[PDF](426.7KB)
A posteriori error estimates for self-similar solutions to the Euler equations
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Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
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Global attractors for damped semilinear wave equations
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Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
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Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
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Positive solution for a nonlinear stationary Schrödinger-Poisson system in $R^3$
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Traveling wave solutions of a highly nonlinear shallow water equation
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Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus
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Stability and bifurcation on predator-prey systems with nonlocal prey competition
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Classification for positive solutions of degenerate elliptic system
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