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By error, JCR gave DCDS an IF of .976. The correct IF of 1.179 will be included in the September update of JCR.

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

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.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
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Follower, predecessor, and extender set sequences of $ \beta $-shifts
Thomas French
2019, 39(8) : 4331-4344 doi: 10.3934/dcds.2019175 +[Abstract](176) +[HTML](54) +[PDF](430.22KB)
On the vanishing contact structure for viscosity solutions of contact type Hamilton-Jacobi equations I: Cauchy problem
Kai Zhao and Wei Cheng
2019, 39(8) : 4345-4358 doi: 10.3934/dcds.2019176 +[Abstract](212) +[HTML](66) +[PDF](395.67KB)
Weak dispersion for the Dirac equation on asymptotically flat and warped product spaces
Federico Cacciafesta and Anne-Sophie De Suzzoni
2019, 39(8) : 4359-4398 doi: 10.3934/dcds.2019177 +[Abstract](167) +[HTML](62) +[PDF](608.67KB)
Exact solution and instability for geophysical waves at arbitrary latitude
Jifeng Chu, Delia Ionescu-Kruse and Yanjuan Yang
2019, 39(8) : 4399-4414 doi: 10.3934/dcds.2019178 +[Abstract](179) +[HTML](72) +[PDF](481.38KB)
Study of an elliptic partial differential equation modelling the Antarctic Circumpolar Current
Susanna V. Haziot
2019, 39(8) : 4415-4427 doi: 10.3934/dcds.2019179 +[Abstract](110) +[HTML](63) +[PDF](355.49KB)
Existence of solutions for nonlinear operator equations
Yucheng Bu and Yujun Dong
2019, 39(8) : 4429-4441 doi: 10.3934/dcds.2019180 +[Abstract](127) +[HTML](54) +[PDF](413.37KB)
Wind generated equatorial Gerstner-type waves
Anatoly Abrashkin
2019, 39(8) : 4443-4453 doi: 10.3934/dcds.2019181 +[Abstract](85) +[HTML](56) +[PDF](349.36KB)
Weak periodic solutions and numerical case studies of the Fornberg-Whitham equation
Günther Hörmann and Hisashi Okamoto
2019, 39(8) : 4455-4469 doi: 10.3934/dcds.2019182 +[Abstract](90) +[HTML](46) +[PDF](522.95KB)
Geophysical internal equatorial waves of extreme form
Tony Lyons
2019, 39(8) : 4471-4486 doi: 10.3934/dcds.2019183 +[Abstract](88) +[HTML](52) +[PDF](2186.44KB)
A quasi-linear nonlocal Venttsel' problem of Ambrosetti–Prodi type on fractal domains
Maria Rosaria Lancia, Alejandro Vélez-Santiago and Paola Vernole
2019, 39(8) : 4487-4518 doi: 10.3934/dcds.2019184 +[Abstract](136) +[HTML](65) +[PDF](738.95KB)
Benjamin-Ono model of an internal wave under a flat surface
Alan Compelli and Rossen Ivanov
2019, 39(8) : 4519-4532 doi: 10.3934/dcds.2019185 +[Abstract](98) +[HTML](49) +[PDF](351.29KB)
Shallow water models for stratified equatorial flows
Anna Geyer and Ronald Quirchmayr
2019, 39(8) : 4533-4545 doi: 10.3934/dcds.2019186 +[Abstract](95) +[HTML](51) +[PDF](858.78KB)
2d incompressible Euler equations: New explicit solutions
María J. Martín and Jukka Tuomela
2019, 39(8) : 4547-4563 doi: 10.3934/dcds.2019187 +[Abstract](129) +[HTML](63) +[PDF](417.21KB)
On fractional nonlinear Schrödinger equation with combined power-type nonlinearities
Van Duong Dinh and Binhua Feng
2019, 39(8) : 4565-4612 doi: 10.3934/dcds.2019188 +[Abstract](140) +[HTML](54) +[PDF](768.09KB)
Chern-Simons gauged sigma model into $ \mathbb{H}^2 $ and its self-dual equations
Kwangseok Choe and Hyungjin Huh
2019, 39(8) : 4613-4646 doi: 10.3934/dcds.2019189 +[Abstract](100) +[HTML](73) +[PDF](650.93KB)
Minimality, distality and equicontinuity for semigroup actions on compact Hausdorff spaces
Joseph Auslander and Xiongping Dai
2019, 39(8) : 4647-4711 doi: 10.3934/dcds.2019190 +[Abstract](110) +[HTML](58) +[PDF](967.32KB)
Steady periodic equatorial water waves with vorticity
Jifeng Chu and Joachim Escher
2019, 39(8) : 4713-4729 doi: 10.3934/dcds.2019191 +[Abstract](107) +[HTML](73) +[PDF](466.96KB)
Infinity-harmonic potentials and their streamlines
Erik Lindgren and Peter Lindqvist
2019, 39(8) : 4731-4746 doi: 10.3934/dcds.2019192 +[Abstract](81) +[HTML](45) +[PDF](995.37KB)
On stratified water waves with critical layers and Coriolis forces
Miles H. Wheeler
2019, 39(8) : 4747-4770 doi: 10.3934/dcds.2019193 +[Abstract](97) +[HTML](57) +[PDF](563.71KB)
Study of a nonlinear boundary-value problem of geophysical relevance
Kateryna Marynets
2019, 39(8) : 4771-4781 doi: 10.3934/dcds.2019194 +[Abstract](105) +[HTML](53) +[PDF](354.16KB)
On an exact solution of a nonlinear three-dimensional model in ocean flows with equatorial undercurrent and linear variation in density
Biswajit Basu
2019, 39(8) : 4783-4796 doi: 10.3934/dcds.2019195 +[Abstract](99) +[HTML](60) +[PDF](375.76KB)
Convergence and center manifolds for differential equations driven by colored noise
Jun Shen, Kening Lu and Bixiang Wang
2019, 39(8) : 4797-4840 doi: 10.3934/dcds.2019196 +[Abstract](105) +[HTML](55) +[PDF](641.61KB)
A random cocycle with non Hölder Lyapunov exponent
Pedro Duarte, Silvius Klein and Manuel Santos
2019, 39(8) : 4841-4861 doi: 10.3934/dcds.2019197 +[Abstract](110) +[HTML](45) +[PDF](454.35KB)
Regularity and weak comparison principles for double phase quasilinear elliptic equations
Giuseppe Riey
2019, 39(8) : 4863-4873 doi: 10.3934/dcds.2019198 +[Abstract](113) +[HTML](60) +[PDF](429.8KB)
The Chern-Simons-Higgs and the Chern-Simons-Dirac equations in Fourier-Lebesgue spaces
Hartmut Pecher
2019, 39(8) : 4875-4893 doi: 10.3934/dcds.2019199 +[Abstract](100) +[HTML](57) +[PDF](461.69KB)
Prescribed energy connecting orbits for gradient systems
Francesca Alessio, Piero Montecchiari and Andres Zuniga
2019, 39(8) : 4895-4928 doi: 10.3934/dcds.2019200 +[Abstract](102) +[HTML](45) +[PDF](1627.83KB)
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](2724) +[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](3866) +[PDF](246.2KB) Cited By(153)
Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
Xiaoyue Li and Xuerong Mao
2009, 24(2) : 523-545 doi: 10.3934/dcds.2009.24.523 +[Abstract](3616) +[PDF](262.8KB) Cited By(142)
Remarks on regularities for the 3D MHD equations
Yong Zhou
2005, 12(5) : 881-886 doi: 10.3934/dcds.2005.12.881 +[Abstract](1899) +[PDF](176.3KB) Cited By(141)
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Jie Shen and Xiaofeng Yang
2010, 28(4) : 1669-1691 doi: 10.3934/dcds.2010.28.1669 +[Abstract](2797) +[PDF](382.7KB) Cited By(133)
The problem Of blow-up in nonlinear parabolic equations
Victor A. Galaktionov and Juan-Luis Vázquez
2002, 8(2) : 399-433 doi: 10.3934/dcds.2002.8.399 +[Abstract](2733) +[PDF](369.4KB) Cited By(113)
Positive solution for a nonlinear stationary Schrödinger-Poisson system in $R^3$
Zhengping Wang and Huan-Song Zhou
2007, 18(4) : 809-816 doi: 10.3934/dcds.2007.18.809 +[Abstract](1923) +[PDF](153.0KB) Cited By(89)
BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity
Zhen Lei and Yi Zhou
2009, 25(2) : 575-583 doi: 10.3934/dcds.2009.25.575 +[Abstract](1948) +[PDF](159.5KB) Cited By(82)
Global stability for damped Timoshenko systems
J.E. Muñoz Rivera and Reinhard Racke
2003, 9(6) : 1625-1639 doi: 10.3934/dcds.2003.9.1625 +[Abstract](2116) +[PDF](167.1KB) Cited By(76)
Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces
Songsong Lu, Hongqing Wu and Chengkui Zhong
2005, 13(3) : 701-719 doi: 10.3934/dcds.2005.13.701 +[Abstract](2097) +[PDF](263.7KB) Cited By(74)
Regularity and classification of solutions to static Hartree equations involving fractional Laplacians
Wei Dai, Jiahui Huang, Yu Qin, Bo Wang and Yanqin Fang
2019, 39(3) : 1389-1403 doi: 10.3934/dcds.2018117 +[Abstract](2525) +[HTML](777) +[PDF](472.85KB) PDF Downloads(371)
Traveling wave solutions of a highly nonlinear shallow water equation
Anna Geyer and Ronald Quirchmayr
2018, 38(3) : 1567-1604 doi: 10.3934/dcds.2018065 +[Abstract](3175) +[HTML](1655) +[PDF](12373.99KB) PDF Downloads(294)
On a class of non-local elliptic equations with asymptotically linear term
Yuanhong Wei and Xifeng Su
2018, 38(12) : 6287-6304 doi: 10.3934/dcds.2018154 +[Abstract](1804) +[HTML](489) +[PDF](442.05KB) PDF Downloads(216)
Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus
Ruofei Yao, Yi Li and Hongbin Chen
2019, 39(3) : 1585-1594 doi: 10.3934/dcds.2018122 +[Abstract](2029) +[HTML](623) +[PDF](388.54KB) PDF Downloads(206)
Some questions looking for answers in dynamical systems
Carles Simó
2018, 38(12) : 6215-6239 doi: 10.3934/dcds.2018267 +[Abstract](1359) +[HTML](220) +[PDF](531.03KB) PDF Downloads(204)
Classification for positive solutions of degenerate elliptic system
Yuxia Guo and Jianjun Nie
2019, 39(3) : 1457-1475 doi: 10.3934/dcds.2018130 +[Abstract](1662) +[HTML](543) +[PDF](412.94KB) PDF Downloads(196)
Weakly mixing diffeomorphisms preserving a measurable Riemannian metric with prescribed Liouville rotation behavior
Roland Gunesch and Philipp Kunde
2018, 38(4) : 1615-1655 doi: 10.3934/dcds.2018067 +[Abstract](2181) +[HTML](451) +[PDF](683.82KB) PDF Downloads(194)
The two membranes problem for fully nonlinear operators
Luis Caffarelli, Luis Duque and Hernán Vivas
2018, 38(12) : 6015-6027 doi: 10.3934/dcds.2018152 +[Abstract](1722) +[HTML](385) +[PDF](364.45KB) PDF Downloads(192)
Attainability of the fractional hardy constant with nonlocal mixed boundary conditions: Applications
Boumediene Abdellaoui, Ahmed Attar, Abdelrazek Dieb and Ireneo Peral
2018, 38(12) : 5963-5991 doi: 10.3934/dcds.2018131 +[Abstract](1810) +[HTML](432) +[PDF](521.23KB) PDF Downloads(181)
On the universality of the incompressible Euler equation on compact manifolds
Terence Tao
2018, 38(3) : 1553-1565 doi: 10.3934/dcds.2018064 +[Abstract](1899) +[HTML](336) +[PDF](422.44KB) PDF Downloads(175)

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