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Communications on Pure & Applied Analysis (ISSN 1534-0392) is published monthly. CPAA is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included. It features recent development in analysis and its applications, with a central theme on theoretical and numeric differential equations and applications. It is edited by some leading researchers to guarantee the journal's highest standard and closest link to the scientific communities.


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Low regularity well-posedness of Hartree type Dirac equations in 2, 3-dimensions
Kiyeon Lee
2021, 20(11) : 3667-3686 doi: 10.3934/cpaa.2021126 +[Abstract](289) +[HTML](161) +[PDF](477.29KB)
A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime
Makram Hamouda, Mohamed Ali Hamza and Alessandro Palmieri
2021, 20(11) : 3687-3705 doi: 10.3934/cpaa.2021127 +[Abstract](290) +[HTML](152) +[PDF](446.79KB)
Normalized solutions of supercritical nonlinear fractional Schrödinger equation with potential
Songbai Peng and Aliang Xia
2021, 20(11) : 3707-3728 doi: 10.3934/cpaa.2021128 +[Abstract](364) +[HTML](183) +[PDF](482.93KB)
Attractors and pullback dynamics for non-autonomous piezoelectric system with magnetic and thermal effects
Mirelson M. Freitas, Anderson J. A. Ramos, Manoel J. Dos Santos and Eraldo R. N. Fonseca
2021, 20(11) : 3729-3749 doi: 10.3934/cpaa.2021129 +[Abstract](402) +[HTML](165) +[PDF](480.1KB)
Existence and multiplicity for Hamilton-Jacobi-Bellman equation
Bian-Xia Yang, Shanshan Gu and Guowei Dai
2021, 20(11) : 3751-3777 doi: 10.3934/cpaa.2021130 +[Abstract](382) +[HTML](154) +[PDF](595.71KB)
Continuous solution for a non-linear eikonal system
Ahmad El Hajj and Aya Oussaily
2021, 20(11) : 3779-3807 doi: 10.3934/cpaa.2021131 +[Abstract](287) +[HTML](154) +[PDF](656.87KB)
Global boundedness of radial solutions to a parabolic-elliptic chemotaxis system with flux limitation and nonlinear signal production
Hong Yi, Chunlai Mu, Shuyan Qiu and Lu Xu
2021, 20(11) : 3809-3833 doi: 10.3934/cpaa.2021133 +[Abstract](264) +[HTML](121) +[PDF](513.88KB)
Liouville-type theorem for higher-order Hardy-Hénon system
Kui Li and Zhitao Zhang
2021, 20(11) : 3835-3853 doi: 10.3934/cpaa.2021134 +[Abstract](251) +[HTML](131) +[PDF](441.69KB)
Bounds for subcritical best Sobolev constants in W1, p
Lele Du
2021, 20(11) : 3855-3870 doi: 10.3934/cpaa.2021135 +[Abstract](237) +[HTML](146) +[PDF](398.1KB)
Limit cycles of piecewise polynomial differential systems with the discontinuity line xy = 0
Tao Li and Jaume Llibre
2021, 20(11) : 3871-3893 doi: 10.3934/cpaa.2021136 +[Abstract](280) +[HTML](153) +[PDF](519.43KB)
Dynamics of solutions to a semilinear plate equation with memory
Jinxing Liu, Xiongrui Wang, Jun Zhou and Xu Liu
2021, 20(11) : 3895-3920 doi: 10.3934/cpaa.2021137 +[Abstract](264) +[HTML](159) +[PDF](604.28KB)
Analysis of a diffusive cholera model incorporating latency and bacterial hyperinfectivity
Wei Yang and Jinliang Wang
2021, 20(11) : 3921-3941 doi: 10.3934/cpaa.2021138 +[Abstract](217) +[HTML](140) +[PDF](485.03KB)
Damped Klein-Gordon equation with variable diffusion coefficient
Qinghua Luo
2021, 20(11) : 3943-3958 doi: 10.3934/cpaa.2021139 +[Abstract](205) +[HTML](133) +[PDF](387.85KB)
Interplay of random inputs and adaptive couplings in the Winfree model
Seung-Yeal Ha, Doheon Kim and Bora Moon
2021, 20(11) : 3959-3990 doi: 10.3934/cpaa.2021140 +[Abstract](194) +[HTML](137) +[PDF](558.73KB)
Critical polyharmonic systems and optimal partitions
Mónica Clapp, Juan Carlos Fernández and Alberto Saldaña
2021, 20(11) : 3991-4007 doi: 10.3934/cpaa.2021141 +[Abstract](201) +[HTML](130) +[PDF](450.6KB)
Stability of current density impedance imaging II
Amir Moradifam and Robert Lopez
2021, 20(11) : 4009-4025 doi: 10.3934/cpaa.2021142 +[Abstract](241) +[HTML](128) +[PDF](394.84KB)
Uniqueness and sign properties of minimizers in a quasilinear indefinite problem
Uriel Kaufmann, Humberto Ramos Quoirin and Kenichiro Umezu
2021doi: 10.3934/10.3934/cpaa.2021078 +[Abstract](366) +[HTML](233) +[PDF](319.8KB)
On the attractor for a semilinear wave equation with variable coefficients and nonlinear boundary dissipation
Jiacheng Wang and Peng-Fei Yao
2021doi: 10.3934/cpaa.2021043 +[Abstract](581) +[HTML](287) +[PDF](317.63KB)
Stabilized finite element methods based on multiscale enrichment for Allen-Cahn and Cahn-Hilliard equations
Juan Wen, Yaling He, Yinnian He and Kun Wang
2021doi: 10.3934/cpaa.2021074 +[Abstract](519) +[HTML](218) +[PDF](3024.82KB)
On the even solutions of the Toda system: a degree argument approach
Yong Liu, Jing Tian and Xuelin Yong
2021doi: 10.3934/cpaa.2021075 +[Abstract](411) +[HTML](237) +[PDF](782.03KB)
Hadamard Semidifferential, Oriented Distance Function, and some Applications
Michel C. Delfour
2021doi: 10.3934/cpaa.2021076 +[Abstract](516) +[HTML](239) +[PDF](482.37KB)
Analysis of COVID-19 epidemic transmission trend based on a time-delayed dynamic model
Tailei Zhang and Zhimin Li
2021doi: 10.3934/cpaa.2021088 +[Abstract](483) +[HTML](309) +[PDF](468.47KB)
Data-driven optimal control of a seir model for COVID-19
Hailiang Liu and Xuping Tian
2021doi: 10.3934/cpaa.2021093 +[Abstract](485) +[HTML](221) +[PDF](1372.32KB)
A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion
Jisheng Kou, Huangxin Chen, Xiuhua Wang and Shuyu Sun
2021doi: 10.3934/cpaa.2021094 +[Abstract](398) +[HTML](269) +[PDF](1366.37KB)
Ground state solutions for the fractional problems with dipole-type potential and critical exponent
Yu Su and Zhaosheng Feng
2021doi: 10.3934/cpaa.2021111 +[Abstract](339) +[HTML](183) +[PDF](326.3KB)
An indirect BIE free of degenerate scales
Jeng-Tzong Chen, Shing-Kai Kao, Jeng-Hong Kao and Wei-Chen Tai
2021doi: 10.3934/cpaa.2021114 +[Abstract](311) +[HTML](125) +[PDF](1662.62KB)
Dynamics of solitary waves and periodic waves for a generalized KP-MEW-Burgers equation with damping
Zengji Du, Xiaojie Lin and Yulin Ren
2021doi: 10.3934/cpaa.2021118 +[Abstract](258) +[HTML](178) +[PDF](354.38KB)
Semi-discrete and fully discrete HDG methods for Burgers' equation
Zimo Zhu, Gang Chen and Xiaoping Xie
2021doi: 10.3934/cpaa.2021132 +[Abstract](338) +[HTML](162) +[PDF](488.08KB)
A multiparameter fractional Laplace problem with semipositone nonlinearity
R. Dhanya and Sweta Tiwari
2021doi: 10.3934/cpaa.2021143 +[Abstract](256) +[HTML](123) +[PDF](437.02KB)
Extremal solution and Liouville theorem for anisotropic elliptic equations
Yuan Li
2021doi: 10.3934/cpaa.2021144 +[Abstract](280) +[HTML](126) +[PDF](469.9KB)
Spreading speed and periodic traveling waves of a time periodic and diffusive SI epidemic model with demographic structure
Shuang-Ming Wang, Zhaosheng Feng, Zhi-Cheng Wang and Liang Zhang
2021doi: 10.3934/cpaa.2021145 +[Abstract](294) +[HTML](148) +[PDF](502.96KB)
Invasion waves for a nonlocal dispersal predator-prey model with two predators and one prey
Feiying Yang, Wantong Li and Renhu Wang
2021doi: 10.3934/cpaa.2021146 +[Abstract](200) +[HTML](100) +[PDF](435.17KB)
Multiplicity of positive solutions to semi-linear elliptic problems on metric graphs
Masataka Shibata
2021doi: 10.3934/cpaa.2021147 +[Abstract](175) +[HTML](80) +[PDF](422.3KB)
Sharp gradient estimates on weighted manifolds with compact boundary
Ha Tuan Dung, Nguyen Thac Dung and Jiayong Wu
2021doi: 10.3934/cpaa.2021148 +[Abstract](256) +[HTML](110) +[PDF](327.32KB)
Classification of positive radial solutions to a weighted biharmonic equation
Yuhao Yan
2021doi: 10.3934/cpaa.2021149 +[Abstract](187) +[HTML](93) +[PDF](390.51KB)
Dynamical analysis in disease transmission and final epidemic size
Daifeng Duan, Cuiping Wang and Yuan Yuan
2021doi: 10.3934/cpaa.2021150 +[Abstract](190) +[HTML](82) +[PDF](961.2KB)
The Cauchy problem of a two-phase flow model for a mixture of non-interacting compressible fluids
Zhen Cheng and Wenjun Wang
2021doi: 10.3934/cpaa.2021151 +[Abstract](158) +[HTML](82) +[PDF](432.78KB)
Nondegeneracy of solutions for a class of cooperative systems on $ \mathbb{R}^n $
Marcello Lucia and Guido Sweers
2021doi: 10.3934/cpaa.2021152 +[Abstract](167) +[HTML](85) +[PDF](477.44KB)
Cesaro summation by spheres of lattice sums and Madelung constants
Benjamin Galbally and Sergey Zelik
2021doi: 10.3934/cpaa.2021153 +[Abstract](133) +[HTML](65) +[PDF](678.39KB)
Spatial dynamic analysis for COVID-19 epidemic model with diffusion and Beddington-DeAngelis type incidence
Tao Zheng, Yantao Luo, Xinran Zhou, Long Zhang and Zhidong Teng
2021doi: 10.3934/cpaa.2021154 +[Abstract](249) +[HTML](106) +[PDF](1057.49KB)
Transmission dynamics and high infectiousness of Coronavirus Disease 2019
Shunxiang Huang, Lin Wu, Jing Li, Ming-Zhen Xin, Yingying Wang, Xingjie Hao, Zhongyi Wang, Qihong Deng and Bin-Guo Wang
2021doi: 10.3934/cpaa.2021155 +[Abstract](181) +[HTML](92) +[PDF](1835.77KB)
Uniform stability of the relativistic Cucker-Smale model and its application to a mean-field limit
Hyunjin Ahn, Seung-Yeal Ha and Jeongho Kim
2021doi: 10.3934/cpaa.2021156 +[Abstract](166) +[HTML](78) +[PDF](472.85KB)
Asymptotic expansion of the ground state energy for nonlinear Schrödinger system with three wave interaction
Kazuhiro Kurata and Yuki Osada
2021doi: 10.3934/cpaa.2021157 +[Abstract](153) +[HTML](64) +[PDF](361.97KB)
Controllability and stabilization of gravity-capillary surface water waves in a basin
Jing Cui, Guangyue Gao and Shu-Ming Sun
2021doi: 10.3934/cpaa.2021158 +[Abstract](168) +[HTML](80) +[PDF](472.33KB)
Periodic solutions for a class of second-order differential delay equations
Xuan Wu and Huafeng Xiao
2021doi: 10.3934/cpaa.2021159 +[Abstract](217) +[HTML](75) +[PDF](401.4KB)
Partial regularity result for non-autonomous elliptic systems with general growth
Teresa Isernia, Chiara Leone and Anna Verde
2021doi: 10.3934/cpaa.2021160 +[Abstract](161) +[HTML](70) +[PDF](541.18KB)
Local well-posedness for the Zakharov system in dimension $ d = 2, 3 $
Zijun Chen and Shengkun Wu
2021doi: 10.3934/cpaa.2021161 +[Abstract](156) +[HTML](72) +[PDF](474.29KB)
Time periodic solution to a two-species chemotaxis-Stokes system with $ p $-Laplacian diffusion
Chengxin Du and Changchun Liu
2021doi: 10.3934/cpaa.2021162 +[Abstract](231) +[HTML](116) +[PDF](451.4KB)
Semilinear Schrödinger evolution equations with inverse-square and harmonic potentials via pseudo-conformal symmetry
Toshiyuki Suzuki
2021doi: 10.3934/cpaa.2021163 +[Abstract](154) +[HTML](74) +[PDF](498.94KB)
Green's function for second order parabolic equations with singular lower order coefficients
Seick Kim and Longjuan Xu
2021doi: 10.3934/cpaa.2021164 +[Abstract](140) +[HTML](59) +[PDF](486.53KB)
Radial quasilinear elliptic problems with singular or vanishing potentials
Marino Badiale, Michela Guida and Sergio Rolando
2021doi: 10.3934/cpaa.2021165 +[Abstract](128) +[HTML](56) +[PDF](450.67KB)
Periodic solutions with prescribed minimal period for second order even Hamiltonian systems
Juhong Kuang, Weiyi Chen and Zhiming Guo
2021doi: 10.3934/cpaa.2021166 +[Abstract](163) +[HTML](64) +[PDF](362.8KB)
Singular limit for reactive transport through a thin heterogeneous layer including a nonlinear diffusion coefficient
Markus Gahn
2021doi: 10.3934/cpaa.2021167 +[Abstract](122) +[HTML](66) +[PDF](482.89KB)
Regularity and existence of positive solutions for a fractional system
Ran Zhuo and Yan Li
2021doi: 10.3934/cpaa.2021168 +[Abstract](123) +[HTML](67) +[PDF](425.36KB)
On local well-posedness of logarithmic inviscid regularizations of generalized SQG equations in borderline Sobolev spaces
Michael S. Jolly, Anuj Kumar and Vincent R. Martinez
2021doi: 10.3934/cpaa.2021169 +[Abstract](155) +[HTML](62) +[PDF](490.38KB)
Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru
Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh and Rana Parshad
2021doi: 10.3934/cpaa.2021170 +[Abstract](72) +[HTML](113) +[PDF](2342.85KB)
Quantitative analysis of a system of integral equations with weight on the upper half space
Sufang Tang and Jingbo Dou
2021doi: 10.3934/cpaa.2021171 +[Abstract](126) +[HTML](55) +[PDF](435.79KB)
Singular solutions of a Hénon equation involving a nonlinear gradient term
Craig Cowan and Abdolrahman Razani
2021doi: 10.3934/cpaa.2021172 +[Abstract](122) +[HTML](56) +[PDF](437.55KB)
Marcinkiewicz integral operators along twisted surfaces
Ahmad Al-Salman
2021doi: 10.3934/cpaa.2021173 +[Abstract](154) +[HTML](60) +[PDF](525.53KB)
Self-Improving inequalities for bounded weak solutions to nonlocal double phase equations
James M. Scott and Tadele Mengesha
2021doi: 10.3934/cpaa.2021174 +[Abstract](65) +[HTML](19) +[PDF](523.35KB)
Large deviation principle for stochastic Burgers type equation with reflection
Ran Wang, Jianliang Zhai and Shiling Zhang
2021doi: 10.3934/cpaa.2021175 +[Abstract](71) +[HTML](22) +[PDF](538.49KB)
A priori estimates for the Fractional p-Laplacian with nonlocal Neumann boundary conditions and applications
Dimitri Mugnai, Kanishka Perera and Edoardo Proietti Lippi
2021doi: 10.3934/cpaa.2021177 +[Abstract](14) +[HTML](9) +[PDF](428.28KB)
Inverse scattering transform and soliton solutions of an integrable nonlocal Hirota equation
Yuan Li and Shou-Fu Tian
2021doi: 10.3934/cpaa.2021178 +[Abstract](13) +[HTML](10) +[PDF](606.92KB)
Dynamics of an SIRS epidemic model with cross-diffusion
Yaru Hu and Jinfeng Wang
2021doi: 10.3934/cpaa.2021179 +[Abstract](54) +[HTML](13) +[PDF](423.4KB)
Subharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth
Fanfan Chen, Dingbian Qian, Xiying Sun and Yinyin Wu
2021doi: 10.3934/cpaa.2021180 +[Abstract](14) +[HTML](11) +[PDF](451.87KB)
A general multipurpose interpolation procedure: the magic points
Yvon Maday, Ngoc Cuong Nguyen, Anthony T. Patera and S. H. Pau
2009, 8(1) : 383-404 doi: 10.3934/cpaa.2009.8.383 +[Abstract](5802) +[PDF](826.7KB) Cited By(107)
On the stationary solutions of generalized reaction diffusion equations with $p\& q$-Laplacian
L. Cherfils and Y. Il'yasov
2005, 4(1) : 9-22 doi: 10.3934/cpaa.2005.4.9 +[Abstract](3705) +[PDF](225.5KB) Cited By(106)
Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term
Chuangxia Huang, Hua Zhang and Lihong Huang
2019, 18(6) : 3337-3349 doi: 10.3934/cpaa.2019150 +[Abstract](3822) +[HTML](241) +[PDF](373.99KB) Cited By(102)
A Brezis-Nirenberg result for non-local critical equations in low dimension
Raffaella Servadei and Enrico Valdinoci
2013, 12(6) : 2445-2464 doi: 10.3934/cpaa.2013.12.2445 +[Abstract](5271) +[PDF](509.5KB) Cited By(93)
Convergence of generalized proximal point algorithms
Giuseppe Marino and Hong-Kun Xu
2004, 3(4) : 791-808 doi: 10.3934/cpaa.2004.3.791 +[Abstract](4978) +[PDF](181.7KB) Cited By(90)
Periodic solutions of nonlinear periodic differential systems with a small parameter
Adriana Buică, Jean–Pierre Françoise and Jaume Llibre
2007, 6(1) : 103-111 doi: 10.3934/cpaa.2007.6.103 +[Abstract](2955) +[PDF](130.3KB) Cited By(79)
The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system$^*$
Lihui Guo, Wancheng Sheng and Tong Zhang
2010, 9(2) : 431-458 doi: 10.3934/cpaa.2010.9.431 +[Abstract](4911) +[PDF](1276.3KB) Cited By(72)
Uniqueness of positive solutions to some coupled nonlinear Schrödinger equations
Juncheng Wei and Wei Yao
2012, 11(3) : 1003-1011 doi: 10.3934/cpaa.2012.11.1003 +[Abstract](3556) +[PDF](366.4KB) Cited By(69)
A Liouville type Theorem for an integral system
Dezhong Chen and Li Ma
2006, 5(4) : 855-859 doi: 10.3934/cpaa.2006.5.855 +[Abstract](4240) +[PDF](102.3KB) Cited By(69)
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions
Gianni Gilardi, A. Miranville and Giulio Schimperna
2009, 8(3) : 881-912 doi: 10.3934/cpaa.2009.8.881 +[Abstract](4075) +[PDF](395.6KB) Cited By(69)
Bifurcation and stability of a two-species diffusive Lotka-Volterra model
Li Ma and Shangjiang Guo
2020, 19(3) : 1205-1232 doi: 10.3934/cpaa.2020056 +[Abstract](2528) +[HTML](89) +[PDF](419.64KB) PDF Downloads(774)
Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis
Norikazu Saito
2012, 11(1) : 339-364 doi: 10.3934/cpaa.2012.11.339 +[Abstract](4576) +[PDF](486.1KB) PDF Downloads(721)
Mean value properties and unique continuation
José G. Llorente
2015, 14(1) : 185-199 doi: 10.3934/cpaa.2015.14.185 +[Abstract](2976) +[PDF](427.4KB) PDF Downloads(664)
The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality
Apala Majumdar
2012, 11(3) : 1303-1337 doi: 10.3934/cpaa.2012.11.1303 +[Abstract](3147) +[PDF](596.9KB) PDF Downloads(592)
Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity
Xiumei Deng and Jun Zhou
2020, 19(2) : 923-939 doi: 10.3934/cpaa.2020042 +[Abstract](2712) +[HTML](105) +[PDF](356.11KB) PDF Downloads(543)
W1, p-estimates for elliptic equations with lower order terms
Byungsoo Kang and Hyunseok Kim
2017, 16(3) : 799-822 doi: 10.3934/cpaa.2017038 +[Abstract](2785) +[HTML](134) +[PDF](491.2KB) PDF Downloads(497)
Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression
Lucian Coroianu, Danilo Costarelli, Sorin G. Gal and Gianluca Vinti
2020, 19(8) : 4213-4225 doi: 10.3934/cpaa.2020189 +[Abstract](1298) +[HTML](86) +[PDF](414.25KB) PDF Downloads(494)
Nonlinear wave equation with both strongly and weakly damped terms: Supercritical initial energy finite time blow up
Yanbing Yang and Runzhang Xu
2019, 18(3) : 1351-1358 doi: 10.3934/cpaa.2019065 +[Abstract](4736) +[HTML](372) +[PDF](342.33KB) PDF Downloads(480)
On a delayed epidemic model with non-instantaneous impulses
Liang Bai, Juan J. Nieto and José M. Uzal
2020, 19(4) : 1915-1930 doi: 10.3934/cpaa.2020084 +[Abstract](1783) +[HTML](169) +[PDF](356.02KB) PDF Downloads(473)
Coupled systems of Hilfer fractional differential inclusions in banach spaces
Saïd Abbas, Mouffak Benchohra and John R. Graef
2018, 17(6) : 2479-2493 doi: 10.3934/cpaa.2018118 +[Abstract](5167) +[HTML](225) +[PDF](328.43KB) PDF Downloads(451)

2020 Impact Factor: 1.916
5 Year Impact Factor: 1.510
2020 CiteScore: 1.9

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