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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.


Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

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Stationary states of the cubic conformal flow on $ \mathbb{S}^3 $
Piotr Bizoń, Dominika Hunik-Kostyra and Dmitry Pelinovsky
2020, 40(1) : 1-32 doi: 10.3934/dcds.2020001 +[Abstract](40) +[HTML](22) +[PDF](572.12KB)
Hereditarily non uniformly perfect non-autonomous Julia sets
Mark Comerford, Rich Stankewitz and Hiroki Sumi
2020, 40(1) : 33-46 doi: 10.3934/dcds.2020002 +[Abstract](35) +[HTML](16) +[PDF](7082.74KB)
Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line
Razvan Mosincat and Haewon Yoon
2020, 40(1) : 47-80 doi: 10.3934/dcds.2020003 +[Abstract](33) +[HTML](16) +[PDF](581.23KB)
Local unstable entropy and local unstable pressure for random partially hyperbolic dynamical systems
Xinsheng Wang, Weisheng Wu and Yujun Zhu
2020, 40(1) : 81-105 doi: 10.3934/dcds.2020004 +[Abstract](29) +[HTML](17) +[PDF](404.01KB)
Regularity of extremal solutions of nonlocal elliptic systems
Mostafa Fazly
2020, 40(1) : 107-131 doi: 10.3934/dcds.2020005 +[Abstract](30) +[HTML](18) +[PDF](456.82KB)
Non-potential and non-radial Dirichlet systems with mean curvature operator in Minkowski space
Daniela Gurban, Petru Jebelean and Cǎlin Şerban
2020, 40(1) : 133-151 doi: 10.3934/dcds.2020006 +[Abstract](51) +[HTML](16) +[PDF](385.42KB)
Discrete N-barrier maximum principle for a lattice dynamical system arising in competition models
Chiun-Chuan Chen, Ting-Yang Hsiao and Li-Chang Hung
2020, 40(1) : 153-187 doi: 10.3934/dcds.2020007 +[Abstract](35) +[HTML](13) +[PDF](369.27KB)
Singularities of certain finite energy solutions to the Navier-Stokes system
Grzegorz Karch, Maria E. Schonbek and Tomas P. Schonbek
2020, 40(1) : 189-206 doi: 10.3934/dcds.2020008 +[Abstract](37) +[HTML](22) +[PDF](381.62KB)
A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors
Marianne Akian, Stéphane Gaubert and Antoine Hochart
2020, 40(1) : 207-231 doi: 10.3934/dcds.2020009 +[Abstract](38) +[HTML](20) +[PDF](434.38KB)
Convergence of the follow-the-leader scheme for scalar conservation laws with space dependent flux
Marco Di Francesco and Graziano Stivaletta
2020, 40(1) : 233-266 doi: 10.3934/dcds.2020010 +[Abstract](34) +[HTML](22) +[PDF](432.07KB)
Almost sure global well posedness for the BBM equation with infinite $ L^{2} $ initial data
Justin Forlano
2020, 40(1) : 267-318 doi: 10.3934/dcds.2020011 +[Abstract](37) +[HTML](20) +[PDF](626.09KB)
A shift map with a discontinuous entropy function
Christian Wolf
2020, 40(1) : 319-329 doi: 10.3934/dcds.2020012 +[Abstract](39) +[HTML](14) +[PDF](348.08KB)
Fermi's golden rule and $ H^1 $ scattering for nonlinear Klein-Gordon equations with metastable states
Xinliang An and Avy Soffer
2020, 40(1) : 331-373 doi: 10.3934/dcds.2020013 +[Abstract](23) +[HTML](14) +[PDF](517.57KB)
Interpolation inequalities in $ \mathrm W^{1,p}( {\mathbb S}^1) $ and carré du champ methods
Jean Dolbeault, Marta García-Huidobro and Rául Manásevich
2020, 40(1) : 375-394 doi: 10.3934/dcds.2020014 +[Abstract](28) +[HTML](14) +[PDF](474.13KB)
Derivation of geostrophic equations as a rigorous limit of compressible rotating and heat conducting fluids with the general initial data
Young-Sam Kwon and Antonin Novotny
2020, 40(1) : 395-421 doi: 10.3934/dcds.2020015 +[Abstract](25) +[HTML](14) +[PDF](679.78KB)
On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations
Jaeseop Ahn, Jimyeong Kim and Ihyeok Seo
2020, 40(1) : 423-439 doi: 10.3934/dcds.2020016 +[Abstract](26) +[HTML](14) +[PDF](371.21KB)
Anosov diffeomorphism with a horseshoe that attracts almost any point
Christian Bonatti, Stanislav Minkov, Alexey Okunev and Ivan Shilin
2020, 40(1) : 441-465 doi: 10.3934/dcds.2020017 +[Abstract](25) +[HTML](16) +[PDF](553.15KB)
Existence of positive solutions for integral systems of the weighted Hardy-Littlewood-Sobolev type
Xiaoqian Liu and Yutian Lei
2020, 40(1) : 467-489 doi: 10.3934/dcds.2020018 +[Abstract](37) +[HTML](14) +[PDF](378.26KB)
Variational principles of invariance pressures on partitions
Xing-Fu Zhong
2020, 40(1) : 491-508 doi: 10.3934/dcds.2020019 +[Abstract](29) +[HTML](15) +[PDF](358.76KB)
Discrete maximal regularity for volterra equations and nonlocal time-stepping schemes
Carlos Lizama and Marina Murillo-Arcila
2020, 40(1) : 509-528 doi: 10.3934/dcds.2020020 +[Abstract](36) +[HTML](20) +[PDF](387.21KB)
Compacton equations and integrability: The rosenau-hyman and Cooper-Shepard-Sodano equations
Rafael Hernández Heredero, Marianna Euler, Norbert Euler and Enrique G. Reyes
2020, 40(1) : 529-548 doi: 10.3934/dcds.2020021 +[Abstract](13) +[HTML](19) +[PDF](381.9KB)
Symmetry and monotonicity properties of singular solutions to some cooperative semilinear elliptic systems involving critical nonlinearities
Francesco Esposito
2020, 40(1) : 549-577 doi: 10.3934/dcds.2020022 +[Abstract](31) +[HTML](22) +[PDF](414.22KB)
Existence and nonexistence of subsolutions for augmented Hessian equations
Limei Dai
2020, 40(1) : 579-596 doi: 10.3934/dcds.2020023 +[Abstract](32) +[HTML](19) +[PDF](363.97KB)
Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential
Hyeongjin Lee, Ihyeok Seo and Jihyeon Seok
2020, 40(1) : 597-608 doi: 10.3934/dcds.2020024 +[Abstract](25) +[HTML](11) +[PDF](331.49KB)
Global stability of Keller–Segel systems in critical Lebesgue spaces
Jie Jiang
2020, 40(1) : 609-634 doi: 10.3934/dcds.2020025 +[Abstract](22) +[HTML](14) +[PDF](460.81KB)
Traveling waves for some nonlocal 1D Gross–Pitaevskii equations with nonzero conditions at infinity
André de Laire and Pierre Mennuni
2020, 40(1) : 635-682 doi: 10.3934/dcds.2020026 +[Abstract](18) +[HTML](20) +[PDF](919.16KB)
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](3580) +[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](4584) +[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](4452) +[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](2460) +[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](4009) +[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](3506) +[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](2530) +[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](2594) +[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](2679) +[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](2755) +[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](3938) +[HTML](779) +[PDF](472.85KB) PDF Downloads(386)
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](4689) +[HTML](2003) +[PDF](12373.99KB) PDF Downloads(335)
On the universality of the incompressible Euler equation on compact manifolds
Terence Tao
2018, 38(3) : 1553-1565 doi: 10.3934/dcds.2018064 +[Abstract](3431) +[HTML](588) +[PDF](422.44KB) PDF Downloads(238)
Some questions looking for answers in dynamical systems
Carles Simó
2018, 38(12) : 6215-6239 doi: 10.3934/dcds.2018267 +[Abstract](2711) +[HTML](230) +[PDF](531.03KB) PDF Downloads(227)
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](3134) +[HTML](489) +[PDF](442.05KB) PDF Downloads(225)
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](3598) +[HTML](629) +[PDF](388.54KB) PDF Downloads(220)
Classification for positive solutions of degenerate elliptic system
Yuxia Guo and Jianjun Nie
2019, 39(3) : 1457-1475 doi: 10.3934/dcds.2018130 +[Abstract](2990) +[HTML](544) +[PDF](412.94KB) PDF Downloads(202)
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](2988) +[HTML](389) +[PDF](364.45KB) PDF Downloads(202)
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](3442) +[HTML](451) +[PDF](683.82KB) PDF Downloads(200)
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](3077) +[HTML](435) +[PDF](521.23KB) PDF Downloads(185)

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