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AIMS joins the mathematics community worldwide in congratulating ProfessorAlessio 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 AIMSconference (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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On mean field systems with multi-classes
Dung Tien Nguyen, Son Luu Nguyen and Nguyen Huu Du
2020, 40(2) : 683-707 doi: 10.3934/dcds.2020057 +[Abstract](133) +[HTML](42) +[PDF](482.1KB)
Global existence for semilinear damped wave equations in relation with the Strauss conjecture
Mengyun Liu and Chengbo Wang
2020, 40(2) : 709-724 doi: 10.3934/dcds.2020058 +[Abstract](92) +[HTML](39) +[PDF](414.52KB)
Random jumps and coalescence in the continuum: Evolution of states of an infinite particle system
Yuri Kozitsky and Krzysztof Pilorz
2020, 40(2) : 725-752 doi: 10.3934/dcds.2020059 +[Abstract](105) +[HTML](45) +[PDF](464.63KB)
The Hausdorff dimension function of the family of conformal iterated function systems of generalized complex continued fractions
Kanji Inui, Hikaru Okada and Hiroki Sumi
2020, 40(2) : 753-766 doi: 10.3934/dcds.2020060 +[Abstract](107) +[HTML](45) +[PDF](322.3KB)
Equilibrium states of almost Anosov diffeomorphisms
Dominic Veconi
2020, 40(2) : 767-780 doi: 10.3934/dcds.2020061 +[Abstract](88) +[HTML](58) +[PDF](323.37KB)
Multiple concentrating solutions for a fractional Kirchhoff equation with magnetic fields
Vincenzo Ambrosio
2020, 40(2) : 781-815 doi: 10.3934/dcds.2020062 +[Abstract](81) +[HTML](37) +[PDF](484.39KB)
A curve of positive solutions for an indefinite sublinear Dirichlet problem
Uriel Kaufmann, Humberto Ramos Quoirin and Kenichiro Umezu
2020, 40(2) : 817-845 doi: 10.3934/dcds.2020063 +[Abstract](102) +[HTML](35) +[PDF](866.92KB)
On the anisotropic Moser-Trudinger inequality for unbounded domains in $ \mathbb R^{n} $
Changliang Zhou and Chunqin Zhou
2020, 40(2) : 847-881 doi: 10.3934/dcds.2020064 +[Abstract](101) +[HTML](52) +[PDF](514.58KB)
Dimensions of $ C^1- $average conformal hyperbolic sets
Juan Wang, Jing Wang, Yongluo Cao and Yun Zhao
2020, 40(2) : 883-905 doi: 10.3934/dcds.2020065 +[Abstract](71) +[HTML](34) +[PDF](403.98KB)
On a class of diffusion-aggregation equations
Yuming Paul Zhang
2020, 40(2) : 907-932 doi: 10.3934/dcds.2020066 +[Abstract](73) +[HTML](32) +[PDF](430.5KB)
Radial solutions of scaling invariant nonlinear elliptic equations with mixed reaction terms
Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro and Laurent Véron
2020, 40(2) : 933-982 doi: 10.3934/dcds.2020067 +[Abstract](86) +[HTML](37) +[PDF](926.28KB)
The Maslov and Morse indices for Sturm-Liouville systems on the half-line
Peter Howard and Alim Sukhtayev
2020, 40(2) : 983-1012 doi: 10.3934/dcds.2020068 +[Abstract](74) +[HTML](35) +[PDF](437.74KB)
Singular limit solutions for a 2-dimensional semilinear elliptic system of Liouville type in some general case
Sami Baraket, Soumaya Sâanouni and Nihed Trabelsi
2020, 40(2) : 1013-1063 doi: 10.3934/dcds.2020069 +[Abstract](87) +[HTML](38) +[PDF](609.72KB)
Unlikely intersections over finite fields: Polynomial orbits in small subgroups
László Mérai and Igor E. Shparlinski
2020, 40(2) : 1065-1073 doi: 10.3934/dcds.2020070 +[Abstract](77) +[HTML](39) +[PDF](305.24KB)
Classification and evolution of bifurcation curves for a one-dimensional Dirichlet-Neumann problem with a specific cubic nonlinearity
Yu-Hao Liang and Shin-Hwa Wang
2020, 40(2) : 1075-1105 doi: 10.3934/dcds.2020071 +[Abstract](71) +[HTML](40) +[PDF](1010.77KB)
Logistic type attraction-repulsion chemotaxis systems with a free boundary or unbounded boundary. I. Asymptotic dynamics in fixed unbounded domain
Lianzhang Bao and Wenxian Shen
2020, 40(2) : 1107-1130 doi: 10.3934/dcds.2020072 +[Abstract](86) +[HTML](39) +[PDF](373.5KB)
On the solvability of singular boundary value problems on the real line in the critical growth case
Stefano Biagi and Teresa Isernia
2020, 40(2) : 1131-1157 doi: 10.3934/dcds.2020073 +[Abstract](81) +[HTML](49) +[PDF](414.31KB)
Lazer-McKenna conjecture for higher order elliptic problem with critical growth
Yuxia Guo and Ting Liu
2020, 40(2) : 1159-1189 doi: 10.3934/dcds.2020074 +[Abstract](94) +[HTML](45) +[PDF](468.38KB)
Measure solutions to a system of continuity equations driven by Newtonian nonlocal interactions
José Antonio Carrillo, Marco Di Francesco, Antonio Esposito, Simone Fagioli and Markus Schmidtchen
2020, 40(2) : 1191-1231 doi: 10.3934/dcds.2020075 +[Abstract](101) +[HTML](41) +[PDF](615.62KB)
Some Liouville-type results for stable solutions involving the mean curvature operator: The radial case
Alberto Farina and Miguel Angel Navarro
2020, 40(2) : 1233-1256 doi: 10.3934/dcds.2020076 +[Abstract](101) +[HTML](32) +[PDF](453.93KB)
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
2019doi: 10.3934/dcds.2019226 +[Abstract](904) +[HTML](308) +[PDF](479.3KB)
Cauchy problem of semilinear inhomogeneous elliptic equations of Matukuma-type with multiple growth terms
Yunfeng Jia, Yi Li, Jianhua Wu and Hong-Kun Xu
2019doi: 10.3934/dcds.2019227 +[Abstract](666) +[HTML](274) +[PDF](399.3KB)
Nondegeneracy of harmonic maps from $ {{\mathbb{R}}^{2}} $ to $ {{\mathbb{S}}^{2}} $
Guoyuan Chen, Yong Liu and Juncheng Wei
2019doi: 10.3934/dcds.2019228 +[Abstract](638) +[HTML](261) +[PDF](370.56KB)
Large time behavior of ODE type solutions to nonlinear diffusion equations
Junyong Eom and Kazuhiro Ishige
2019doi: 10.3934/dcds.2019229 +[Abstract](672) +[HTML](259) +[PDF](359.7KB)
Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature
Tianwen Luo, Tao Tao and Liqun Zhang
2019doi: 10.3934/dcds.2019230 +[Abstract](572) +[HTML](263) +[PDF](431.74KB)
Global stabilization of the full attraction-repulsion Keller-Segel system
Hai-Yang Jin and Zhi-An Wang
2019doi: 10.3934/dcds.2020027 +[Abstract](124) +[HTML](60) +[PDF](378.9KB)
A functional approach towards eigenvalue problems associated with incompressible flow
Shuang Liu and Yuan Lou
2019doi: 10.3934/dcds.2020028 +[Abstract](156) +[HTML](66) +[PDF](449.86KB)
On the viscous Camassa-Holm equations with fractional diffusion
Zaihui Gan, Fanghua Lin and Jiajun Tong
2019doi: 10.3934/dcds.2020029 +[Abstract](128) +[HTML](57) +[PDF](396.85KB)
Refined regularity and stabilization properties in a degenerate haptotaxis system
Michael Winkler and Christian Stinner
2019doi: 10.3934/dcds.2020030 +[Abstract](99) +[HTML](58) +[PDF](383.86KB)
Asymptotic population abundance of a two-patch system with asymmetric diffusion
Mengting Fang, Yuanshi Wang, Mingshu Chen and Donald L. DeAngelis
2019doi: 10.3934/dcds.2020031 +[Abstract](137) +[HTML](86) +[PDF](598.55KB)
Spectral asymptotics of radial solutions and nonradial bifurcation for the Hénon equation
Joel Kübler and Tobias Weth
2019doi: 10.3934/dcds.2020032 +[Abstract](152) +[HTML](62) +[PDF](474.43KB)
Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity
Maho Endo, Yuki Kaneko and Yoshio Yamada
2019doi: 10.3934/dcds.2020033 +[Abstract](212) +[HTML](78) +[PDF](203.66KB)
A Hopf lemma and regularity for fractional $ p $-Laplacians
Wenxiong Chen, Congming Li and Shijie Qi
2019doi: 10.3934/dcds.2020034 +[Abstract](125) +[HTML](55) +[PDF](386.0KB)
Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small
Xueli Bai and Fang Li
2019doi: 10.3934/dcds.2020035 +[Abstract](144) +[HTML](64) +[PDF](366.91KB)
Variational and operator methods for Maxwell-Stokes system
Xing-Bin Pan
2019doi: 10.3934/dcds.2020036 +[Abstract](140) +[HTML](84) +[PDF](542.41KB)
On space-time periodic solutions of the one-dimensional heat equation
Dong-Ho Tsai and Chia-Hsing Nien
2019doi: 10.3934/dcds.2020037 +[Abstract](124) +[HTML](48) +[PDF](426.74KB)
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
2019doi: 10.3934/dcds.2020038 +[Abstract](173) +[HTML](74) +[PDF](825.25KB)
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
2019doi: 10.3934/dcds.2020039 +[Abstract](102) +[HTML](51) +[PDF](458.42KB)
Eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a large zonal domain in the unit sphere
Yoshitsugu Kabeya
2019doi: 10.3934/dcds.2020040 +[Abstract](109) +[HTML](50) +[PDF](369.84KB)
Signed Radon measure-valued solutions of flux saturated scalar conservation laws
Michiel Bertsch, Flavia Smarrazzo, Andrea Terracina and Alberto Tesei
2019doi: 10.3934/dcds.2020041 +[Abstract](119) +[HTML](61) +[PDF](479.51KB)
A stage structured model of delay differential equations for Aedes mosquito population suppression
Mugen Huang, Moxun Tang, Jianshe Yu and Bo Zheng
2019doi: 10.3934/dcds.2020042 +[Abstract](159) +[HTML](107) +[PDF](497.6KB)
Asymmetric dispersal and evolutional selection in two-patch system
Yong-Jung Kim, Hyowon Seo and Changwook Yoon
2019doi: 10.3934/dcds.2020043 +[Abstract](125) +[HTML](99) +[PDF](728.39KB)
Asymptotic homogenization for delay-differential equations and a question of analyticity
John Mallet-Paret and Roger D. Nussbaum
2019doi: 10.3934/dcds.2020044 +[Abstract](116) +[HTML](66) +[PDF](385.81KB)
Sectional symmetry of solutions of elliptic systems in cylindrical domains
Lucio Damascelli and Filomena Pacella
2019doi: 10.3934/dcds.2020045 +[Abstract](108) +[HTML](47) +[PDF](318.6KB)
Evolution equations involving nonlinear truncated Laplacian operators
Matthieu Alfaro and Isabeau Birindelli
2019doi: 10.3934/dcds.2020046 +[Abstract](105) +[HTML](60) +[PDF](361.4KB)
The sign of traveling wave speed in bistable dynamics
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara and Chang-Hong Wu
2019doi: 10.3934/dcds.2020047 +[Abstract](166) +[HTML](89) +[PDF](308.89KB)
The impact of the domain boundary on an inhibitory system: Interior discs and boundary half discs
Xiaofeng Ren and David Shoup
2019doi: 10.3934/dcds.2020048 +[Abstract](109) +[HTML](48) +[PDF](586.41KB)
Spike solutions for a mass conservation reaction-diffusion system
Shin-Ichiro Ei and Shyuh-Yaur Tzeng
2019doi: 10.3934/dcds.2020049 +[Abstract](114) +[HTML](64) +[PDF](355.07KB)
Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach
Qian Liu, Shuang Liu and King-Yeung Lam
2019doi: 10.3934/dcds.2020050 +[Abstract](127) +[HTML](54) +[PDF](748.97KB)
Existence and instability of some nontrivial steady states for the SKT competition model with large cross diffusion
Qing Li and Yaping Wu
2019doi: 10.3934/dcds.2020051 +[Abstract](125) +[HTML](54) +[PDF](676.08KB)
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
2019doi: 10.3934/dcds.2020052 +[Abstract](137) +[HTML](91) +[PDF](484.25KB)
Bifurcation from infinity with applications to reaction-diffusion systems
Chihiro Aida, Chao-Nien Chen, Kousuke Kuto and Hirokazu Ninomiya
2019doi: 10.3934/dcds.2020053 +[Abstract](121) +[HTML](57) +[PDF](355.83KB)
On the spectral theory of positive operators and PDE applications
Kung-Ching Chang, Xuefeng Wang and Xie Wu
2019doi: 10.3934/dcds.2020054 +[Abstract](183) +[HTML](94) +[PDF](436.57KB)
Perturbative techniques for the construction of spike-layers
Andrea Malchiodi
2019doi: 10.3934/dcds.2020055 +[Abstract](115) +[HTML](90) +[PDF](373.27KB)
Monotone and nonmonotone clines with partial panmixia across a geographical barrier
Yantao Wang and Linlin Su
2019doi: 10.3934/dcds.2020056 +[Abstract](110) +[HTML](64) +[PDF](884.4KB)
Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
Joachim Escher, Olaf Lechtenfeld and Zhaoyang Yin
2007, 19(3) : 493-513 doi: 10.3934/dcds.2007.19.493 +[Abstract](3735) +[PDF](233.8KB) Cited By(162)
Global attractors for damped semilinear wave equations
John M. Ball
2004, 10(1&2) : 31-52 doi: 10.3934/dcds.2004.10.31 +[Abstract](4740) +[PDF](246.2KB) Cited By(153)
Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
Xiaoyue Li and Xuerong Mao
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Remarks on regularities for the 3D MHD equations
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2005, 12(5) : 881-886 doi: 10.3934/dcds.2005.12.881 +[Abstract](2621) +[PDF](176.3KB) Cited By(141)
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
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2010, 28(4) : 1669-1691 doi: 10.3934/dcds.2010.28.1669 +[Abstract](4263) +[PDF](382.7KB) Cited By(133)
The problem Of blow-up in nonlinear parabolic equations
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Positive solution for a nonlinear stationary Schrödinger-Poisson system in $R^3$
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BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity
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Global stability for damped Timoshenko systems
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Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces
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Regularity and classification of solutions to static Hartree equations involving fractional Laplacians
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Traveling wave solutions of a highly nonlinear shallow water equation
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On the universality of the incompressible Euler equation on compact manifolds
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Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus
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Some questions looking for answers in dynamical systems
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On a class of non-local elliptic equations with asymptotically linear term
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A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic fisher kpp equation
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Classification for positive solutions of degenerate elliptic system
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The two membranes problem for fully nonlinear operators
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Weakly mixing diffeomorphisms preserving a measurable Riemannian metric with prescribed Liouville rotation behavior
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