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Discrete & Continuous Dynamical Systems (DCDS) publishes peer-reviewed original and expository papers on the theory, methods and applications of analysis, differential equations and dynamical systems. The journal is committed to recording important new methods and 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 the compactness threshold in the critical Kirchhoff equation
Erisa Hasani and Kanishka Perera
2022, 42(1) : 1-19 doi: 10.3934/dcds.2021106 +[Abstract](753) +[HTML](240) +[PDF](413.39KB)
On the number of positive solutions to an indefinite parameter-dependent Neumann problem
Guglielmo Feltrin, Elisa Sovrano and Andrea Tellini
2022, 42(1) : 21-71 doi: 10.3934/dcds.2021107 +[Abstract](439) +[HTML](202) +[PDF](697.04KB)
Upper semicontinuity of pullback attractors for non-autonomous lattice systems under singular perturbations
Na Lei and Shengfan Zhou
2022, 42(1) : 73-108 doi: 10.3934/dcds.2021108 +[Abstract](398) +[HTML](174) +[PDF](528.52KB)
Global existence of solutions to reaction diffusion systems with mass transport type boundary conditions on an evolving domain
Vandana Sharma and Jyotshana V. Prajapat
2022, 42(1) : 109-135 doi: 10.3934/dcds.2021109 +[Abstract](175) +[HTML](73) +[PDF](433.07KB)
A semilinear problem with a gradient term in the nonlinearity
Ignacio Guerra
2022, 42(1) : 137-162 doi: 10.3934/dcds.2021110 +[Abstract](345) +[HTML](175) +[PDF](339.19KB)
Combined effects of singular and exponential nonlinearities in fractional Kirchhoff problems
Tuhina Mukherjee, Patrizia Pucci and Mingqi Xiang
2022, 42(1) : 163-187 doi: 10.3934/dcds.2021111 +[Abstract](372) +[HTML](199) +[PDF](467.36KB)
Orbit counting in polarized dynamical systems
Wade Hindes
2022, 42(1) : 189-210 doi: 10.3934/dcds.2021112 +[Abstract](287) +[HTML](164) +[PDF](493.79KB)
The relaxation limit of bipolar fluid models
Nuno J. Alves and Athanasios E. Tzavaras
2022, 42(1) : 211-237 doi: 10.3934/dcds.2021113 +[Abstract](320) +[HTML](148) +[PDF](372.71KB)
Families of vector fields with many numerical invariants
Nataliya Goncharuk and Yury Kudryashov
2022, 42(1) : 239-259 doi: 10.3934/dcds.2021114 +[Abstract](306) +[HTML](175) +[PDF](417.38KB)
On a curvature flow in a band domain with unbounded boundary slopes
Lixia Yuan and Wei Zhao
2022, 42(1) : 261-283 doi: 10.3934/dcds.2021115 +[Abstract](284) +[HTML](156) +[PDF](504.06KB)
Shadowing for families of endomorphisms of generalized group shifts
Xuan Kien Phung
2022, 42(1) : 285-299 doi: 10.3934/dcds.2021116 +[Abstract](337) +[HTML](143) +[PDF](362.63KB)
Estimates the upper bounds of Dirichlet eigenvalues for fractional Laplacian
Hua Chen and Hong-Ge Chen
2022, 42(1) : 301-317 doi: 10.3934/dcds.2021117 +[Abstract](306) +[HTML](163) +[PDF](417.48KB)
Subhyperbolic rational maps on boundaries of hyperbolic components
Yan Gao, Luxian Yang and Jinsong Zeng
2022, 42(1) : 319-326 doi: 10.3934/dcds.2021118 +[Abstract](307) +[HTML](138) +[PDF](304.0KB)
The geodesic flow on nilpotent Lie groups of steps two and three
Gabriela P. Ovando
2022, 42(1) : 327-352 doi: 10.3934/dcds.2021119 +[Abstract](286) +[HTML](139) +[PDF](450.76KB)
Inducing schemes for multi-dimensional piecewise expanding maps
Peyman Eslami
2022, 42(1) : 353-368 doi: 10.3934/dcds.2021120 +[Abstract](311) +[HTML](150) +[PDF](396.69KB)
Decay estimates for Schrödinger heat semigroup with inverse square potential in Lorentz spaces II
Kazuhiro Ishige and Yujiro Tateishi
2022, 42(1) : 369-401 doi: 10.3934/dcds.2021121 +[Abstract](325) +[HTML](129) +[PDF](517.56KB)
The critical points of the elastic energy among curves pinned at endpoints
Kensuke Yoshizawa
2022, 42(1) : 403-423 doi: 10.3934/dcds.2021122 +[Abstract](308) +[HTML](139) +[PDF](1182.05KB)
The Brinkman-Fourier system with ideal gas equilibrium
Chun Liu and Jan-Eric Sulzbach
2022, 42(1) : 425-462 doi: 10.3934/dcds.2021123 +[Abstract](375) +[HTML](139) +[PDF](425.63KB)
Exact null-controllability of interconnected abstract evolution equations with unbounded input operators
Benzion Shklyar
2022, 42(1) : 463-479 doi: 10.3934/dcds.2021124 +[Abstract](287) +[HTML](132) +[PDF](433.82KB)
A log–exp elliptic equation in the plane
Giovany Figueiredo, Marcelo Montenegro and Matheus F. Stapenhorst
2022, 42(1) : 481-504 doi: 10.3934/dcds.2021125 +[Abstract](381) +[HTML](138) +[PDF](425.74KB)
Exact description of SIR-Bass epidemics on 1D lattices
Gadi Fibich and Samuel Nordmann
2021doi: 10.3934/dcds.2021126 +[Abstract](261) +[HTML](150) +[PDF](460.53KB)
$ W^{1, p} $ estimates for elliptic problems with drift terms in Lipschitz domains
Bojing Shi
2021doi: 10.3934/dcds.2021127 +[Abstract](285) +[HTML](152) +[PDF](362.92KB)
Aubry-Mather theory for contact Hamiltonian systems II
Kaizhi Wang, Lin Wang and Jun Yan
2021doi: 10.3934/dcds.2021128 +[Abstract](234) +[HTML](144) +[PDF](588.98KB)
Realizing arbitrary $d$-dimensional dynamics by renormalization of $C^d$-perturbations of identity
Bassam Fayad and Maria Saprykina
2021doi: 10.3934/dcds.2021129 +[Abstract](225) +[HTML](126) +[PDF](178.97KB)
Propagating fronts for a viscous Hamer-type system
Giada Cianfarani Carnevale, Corrado Lattanzio and Corrado Mascia
2021doi: 10.3934/dcds.2021130 +[Abstract](217) +[HTML](121) +[PDF](427.65KB)
Forward triplets and topological entropy on trees
Lluís Alsedà, David Juher and Francesc Mañosas
2021doi: 10.3934/dcds.2021131 +[Abstract](233) +[HTML](141) +[PDF](481.04KB)
Pullback attractors for 2D MHD equations on time-varying domains
Daomin Cao, Xiaoya Song and Chunyou Sun
2021doi: 10.3934/dcds.2021132 +[Abstract](240) +[HTML](124) +[PDF](571.28KB)
On the fractional susceptibility function of piecewise expanding maps
Magnus Aspenberg, Viviane Baladi, Juho Leppänen and Tomas Persson
2021doi: 10.3934/dcds.2021133 +[Abstract](257) +[HTML](118) +[PDF](284.65KB)
Generalization of the Winfree model to the high-dimensional sphere and its emergent dynamics
Hansol Park
2021doi: 10.3934/dcds.2021134 +[Abstract](235) +[HTML](119) +[PDF](561.5KB)
Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction
Giovanni Colombo, Paolo Gidoni and Emilio Vilches
2021doi: 10.3934/dcds.2021135 +[Abstract](261) +[HTML](119) +[PDF](536.48KB)
Global existence and convergence to steady states for a predator-prey model with both predator- and prey-taxis
Guoqiang Ren and Bin Liu
2021doi: 10.3934/dcds.2021136 +[Abstract](275) +[HTML](148) +[PDF](511.96KB)
Singular weighted sharp Trudinger-Moser inequalities defined on $ \mathbb{R}^N $ and applications to elliptic nonlinear equations
Sami Aouaoui and Rahma Jlel
2021doi: 10.3934/dcds.2021137 +[Abstract](239) +[HTML](130) +[PDF](613.85KB)
Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms of the circle
Stefano Galatolo and Alfonso Sorrentino
2021doi: 10.3934/dcds.2021138 +[Abstract](225) +[HTML](127) +[PDF](589.44KB)
Cohomology groups, continuous full groups and continuous orbit equivalence of topological Markov shifts
Kengo Matsumoto
2021doi: 10.3934/dcds.2021139 +[Abstract](207) +[HTML](124) +[PDF](352.01KB)
Pure strictly uniform models of non-ergodic measure automorphisms
Tomasz Downarowicz and Benjamin Weiss
2021doi: 10.3934/dcds.2021140 +[Abstract](208) +[HTML](122) +[PDF](1588.76KB)
Global stability solution of the 2D MHD equations with mixed partial dissipation
Yana Guo, Yan Jia and Bo-Qing Dong
2021doi: 10.3934/dcds.2021141 +[Abstract](248) +[HTML](129) +[PDF](307.3KB)
The nonlocal-interaction equation near attracting manifolds
Francesco S. Patacchini and Dejan Slepčev
2021doi: 10.3934/dcds.2021142 +[Abstract](206) +[HTML](116) +[PDF](565.89KB)
Characterizing entropy dimensions of minimal mutidimensional subshifts of finite type
Silvère Gangloff
2021doi: 10.3934/dcds.2021143 +[Abstract](177) +[HTML](85) +[PDF](837.74KB)
Criniferous entire maps with absorbing Cantor bouquets
Leticia Pardo-Simón
2021doi: 10.3934/dcds.2021144 +[Abstract](179) +[HTML](72) +[PDF](736.75KB)
On the improved interior regularity of a boundary value problem modelling the displacement of a linearly elastic elliptic membrane shell subject to an obstacle
Paolo Piersanti
2021doi: 10.3934/dcds.2021145 +[Abstract](161) +[HTML](78) +[PDF](662.54KB)
Periodic and asymptotically periodic fourth-order Schrödinger equations with critical and subcritical growth
Edcarlos D. Silva, Marcos L. M. Carvalho and Claudiney Goulart
2021doi: 10.3934/dcds.2021146 +[Abstract](188) +[HTML](73) +[PDF](572.29KB)
Local well-posedness for the Zakharov system in dimension d ≤ 3
Akansha Sanwal
2021doi: 10.3934/dcds.2021147 +[Abstract](221) +[HTML](82) +[PDF](685.52KB)
Zero-dimensional and symbolic extensions of topological flows
David Burguet and Ruxi Shi
2021doi: 10.3934/dcds.2021148 +[Abstract](164) +[HTML](69) +[PDF](591.74KB)
Two species nonlocal diffusion systems with free boundaries
Yihong Du, Mingxin Wang and Meng Zhao
2021doi: 10.3934/dcds.2021149 +[Abstract](293) +[HTML](119) +[PDF](601.05KB)
Topological mild mixing of all orders along polynomials
Yang Cao and Song Shao
2021doi: 10.3934/dcds.2021150 +[Abstract](108) +[HTML](42) +[PDF](540.61KB)
Regularity for the 3D evolution Navier-Stokes equations under Navier boundary conditions in some Lipschitz domains
Alessio Falocchi and Filippo Gazzola
2021doi: 10.3934/dcds.2021151 +[Abstract](142) +[HTML](42) +[PDF](1295.3KB)
Global $ C^2 $-estimates for smooth solutions to uniformly parabolic equations with Neumann boundary condition
Zhenghuan Gao and Peihe Wang
2021doi: 10.3934/dcds.2021152 +[Abstract](131) +[HTML](43) +[PDF](378.82KB)
Statistics of multipliers for hyperbolic rational maps
Richard Sharp and Anastasios Stylianou
2021doi: 10.3934/dcds.2021153 +[Abstract](160) +[HTML](56) +[PDF](373.75KB)
Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory
Guangcun Lu
2021doi: 10.3934/dcds.2021154 +[Abstract](157) +[HTML](88) +[PDF](789.73KB)
Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems
Guangcun Lu
2021doi: 10.3934/dcds.2021155 +[Abstract](148) +[HTML](54) +[PDF](673.9KB)
Elliptic systems involving Schrödinger operators with vanishing potentials
Juan Arratia, Denilson Pereira and Pedro Ubilla
2021doi: 10.3934/dcds.2021156 +[Abstract](131) +[HTML](45) +[PDF](917.3KB)
Number of bounded distance equivalence classes in hulls of repetitive Delone sets
Dirk Frettlöh, Alexey Garber and Lorenzo Sadun
2021doi: 10.3934/dcds.2021157 +[Abstract](104) +[HTML](40) +[PDF](361.41KB)
Lower bounds for Orlicz eigenvalues
Ariel Salort
2021doi: 10.3934/dcds.2021158 +[Abstract](95) +[HTML](39) +[PDF](444.32KB)
On the structure of $ \alpha $-limit sets of backward trajectories for graph maps
Magdalena Foryś-Krawiec, Jana Hantáková and Piotr Oprocha
2021doi: 10.3934/dcds.2021159 +[Abstract](125) +[HTML](44) +[PDF](593.51KB)
Eternal solutions for a reaction-diffusion equation with weighted reaction
Razvan Gabriel Iagar and Ariel Sánchez
2021doi: 10.3934/dcds.2021160 +[Abstract](140) +[HTML](53) +[PDF](644.0KB)
An Erratum on "Stability and dynamics of a weak viscoelastic system with memory and nonlinear time-varying delay" (Discrete Continuous Dynamic Systems, 40(3), 2020, 1493-1515)
Xin-Guang Yang
2021doi: 10.3934/dcds.2021161 +[Abstract](119) +[HTML](52) +[PDF](143.51KB)
Strong Birkhoff ergodic theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles
Kai Tao
2021doi: 10.3934/dcds.2021162 +[Abstract](83) +[HTML](36) +[PDF](484.18KB)
On long-time asymptotic behavior for solutions to 2D temperature-dependent tropical climate model
Chaoying Li, Xiaojing Xu and Zhuan Ye
2021doi: 10.3934/dcds.2021163 +[Abstract](92) +[HTML](32) +[PDF](411.28KB)
Quantitative destruction of invariant circles
Lin Wang
2021doi: 10.3934/dcds.2021164 +[Abstract](76) +[HTML](31) +[PDF](327.89KB)
Expansive flows on uniform spaces
Se-Hyun Ku
2021doi: 10.3934/dcds.2021165 +[Abstract](99) +[HTML](35) +[PDF](326.81KB)
Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay
Ning Wang and Zhi-Cheng Wang
2021doi: 10.3934/dcds.2021166 +[Abstract](96) +[HTML](32) +[PDF](2777.52KB)
Stability of optimal traffic plans in the irrigation problem
Maria Colombo, Antonio De Rosa, Andrea Marchese, Paul Pegon and Antoine Prouff
2021doi: 10.3934/dcds.2021167 +[Abstract](92) +[HTML](44) +[PDF](375.25KB)
Rigidity, weak mixing, and recurrence in abelian groups
Ethan M. Ackelsberg
2021doi: 10.3934/dcds.2021168 +[Abstract](97) +[HTML](33) +[PDF](514.34KB)
On super-exponential divergence of periodic points for partially hyperbolic systems
Xiaolong Li and Katsutoshi Shinohara
2021doi: 10.3934/dcds.2021169 +[Abstract](83) +[HTML](29) +[PDF](412.02KB)
Nonlinear nonlocal reaction-diffusion problem with local reaction
Aníbal Rodríguez-Bernal and Silvia Sastre-Gómez
2021doi: 10.3934/dcds.2021170 +[Abstract](93) +[HTML](34) +[PDF](500.06KB)
Instability of the soliton for the focusing, mass-critical generalized KdV equation
Benjamin Dodson and Cristian Gavrus
2021doi: 10.3934/dcds.2021171 +[Abstract](74) +[HTML](31) +[PDF](487.6KB)
Multiplicity of closed Reeb orbits on dynamically convex $ \mathbb{R}P^{2n-1} $ for $ n\geq2 $
Hui Liu and Ling Zhang
2021doi: 10.3934/dcds.2021172 +[Abstract](93) +[HTML](33) +[PDF](389.67KB)
Fujita type results for quasilinear parabolic inequalities with nonlocal terms
Roberta Filippucci and Marius Ghergu
2021doi: 10.3934/dcds.2021173 +[Abstract](79) +[HTML](34) +[PDF](358.71KB)
On $ L^1 $ estimates of solutions of compressible viscoelastic system
Yusuke Ishigaki
2021doi: 10.3934/dcds.2021174 +[Abstract](65) +[HTML](27) +[PDF](181.31KB)
Sublacunary sets and interpolation sets for nilsequences
Anh N. Le
2021doi: 10.3934/dcds.2021175 +[Abstract](82) +[HTML](33) +[PDF](356.98KB)
Random attractors for dissipative systems with rough noises
Luu Hoang Duc
2021doi: 10.3934/dcds.2021176 +[Abstract](91) +[HTML](81) +[PDF](441.23KB)
Boltzmann-Grad limit of a hard sphere system in a box with isotropic boundary conditions
Corentin Le Bihan
2021doi: 10.3934/dcds.2021177 +[Abstract](68) +[HTML](25) +[PDF](566.6KB)
A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem
Muhammad Hamid and Wei Wang
2021doi: 10.3934/dcds.2021178 +[Abstract](65) +[HTML](28) +[PDF](367.98KB)
Global propagation of singularities for discounted Hamilton-Jacobi equations
Cui Chen, Jiahui Hong and Kai Zhao
2021doi: 10.3934/dcds.2021179 +[Abstract](64) +[HTML](26) +[PDF](396.93KB)
High and low perturbations of Choquard equations with critical reaction and variable growth
Youpei Zhang, Xianhua Tang and Vicenţiu D. Rădulescu
2021doi: 10.3934/dcds.2021180 +[Abstract](67) +[HTML](23) +[PDF](475.49KB)
Existence of minimizers for one-dimensional vectorial non-semicontinuous functionals with second order lagrangian
Sandro Zagatti
2021doi: 10.3934/dcds.2021181 +[Abstract](72) +[HTML](25) +[PDF](360.96KB)
Crystalline flow starting from a general polygon
Mi-Ho Giga, Yoshikazu Giga, Ryo Kuroda and Yusuke Ochiai
2021doi: 10.3934/dcds.2021182 +[Abstract](70) +[HTML](18) +[PDF](536.0KB)
Equidistribution of translates of a homogeneous measure on the Borel–Serre compactification
Runlin Zhang
2021doi: 10.3934/dcds.2021183 +[Abstract](67) +[HTML](21) +[PDF](428.33KB)
Liouville-type theorem for high order degenerate Lane-Emden system
Yuxia Guo and Ting Liu
2021doi: 10.3934/dcds.2021184 +[Abstract](71) +[HTML](21) +[PDF](440.63KB)
Geodesic planes in geometrically finite manifolds-corrigendum
Osama Khalil
2021doi: 10.3934/dcds.2021185 +[Abstract](61) +[HTML](15) +[PDF](147.87KB)
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](8942) +[PDF](382.7KB) Cited By(319)
Variational methods for non-local operators of elliptic type
Raffaella Servadei and Enrico Valdinoci
2013, 33(5) : 2105-2137 doi: 10.3934/dcds.2013.33.2105 +[Abstract](5929) +[PDF](418.8KB) Cited By(292)
Global well-posedness of the viscous Boussinesq equations
Thomas Y. Hou and Congming Li
2005, 12(1) : 1-12 doi: 10.3934/dcds.2005.12.1 +[Abstract](4495) +[PDF](203.5KB) Cited By(209)
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](8107) +[PDF](262.8KB) Cited By(202)
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](5848) +[PDF](233.8KB) Cited By(202)
Global attractors for damped semilinear wave equations
John M. Ball
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Partial regularity of the dynamic system modeling the flow of liquid crystals
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The problem Of blow-up in nonlinear parabolic equations
Victor A. Galaktionov and Juan-Luis Vázquez
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Remarks on regularities for the 3D MHD equations
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Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
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The problem Of blow-up in nonlinear parabolic equations
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Some questions looking for answers in dynamical systems
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The vorticity equation on a rotating sphere and the shallow fluid approximation
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Conditional measures and conditional expectation; Rohlin's Disintegration Theorem
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Differentiability of the Hartman--Grobman linearization
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Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Jie Shen and Xiaofeng Yang
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Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
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On the spectral theory of positive operators and PDE applications
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On Geometric Mechanics
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Regularity and classification of solutions to static Hartree equations involving fractional Laplacians
Wei Dai, Jiahui Huang, Yu Qin, Bo Wang and Yanqin Fang
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2020 Impact Factor: 1.392
5 Year Impact Factor: 1.610
2020 CiteScore: 2.2

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