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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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A multiparameter fractional Laplace problem with semipositone nonlinearity
R. Dhanya and Sweta Tiwari
2021, 20(12) : 4043-4061 doi: 10.3934/cpaa.2021143 +[Abstract](380) +[HTML](180) +[PDF](204.81KB)
Extremal solution and Liouville theorem for anisotropic elliptic equations
Yuan Li
2021, 20(12) : 4063-4082 doi: 10.3934/cpaa.2021144 +[Abstract](419) +[HTML](178) +[PDF](205.68KB)
Invasion waves for a nonlocal dispersal predator-prey model with two predators and one prey
Feiying Yang, Wantong Li and Renhu Wang
2021, 20(12) : 4083-4105 doi: 10.3934/cpaa.2021146 +[Abstract](313) +[HTML](148) +[PDF](210.96KB)
Multiplicity of positive solutions to semi-linear elliptic problems on metric graphs
Masataka Shibata
2021, 20(12) : 4107-4126 doi: 10.3934/cpaa.2021147 +[Abstract](285) +[HTML](128) +[PDF](203.48KB)
Sharp gradient estimates on weighted manifolds with compact boundary
Ha Tuan Dung, Nguyen Thac Dung and Jiayong Wu
2021, 20(12) : 4127-4138 doi: 10.3934/cpaa.2021148 +[Abstract](441) +[HTML](164) +[PDF](145.9KB)
Classification of positive radial solutions to a weighted biharmonic equation
Yuhao Yan
2021, 20(12) : 4139-4154 doi: 10.3934/cpaa.2021149 +[Abstract](297) +[HTML](141) +[PDF](174.69KB)
The Cauchy problem of a two-phase flow model for a mixture of non-interacting compressible fluids
Zhen Cheng and Wenjun Wang
2021, 20(12) : 4155-4176 doi: 10.3934/cpaa.2021151 +[Abstract](268) +[HTML](127) +[PDF](203.19KB)
Nondegeneracy of solutions for a class of cooperative systems on $ \mathbb{R}^n $
Marcello Lucia and Guido Sweers
2021, 20(12) : 4177-4193 doi: 10.3934/cpaa.2021152 +[Abstract](277) +[HTML](135) +[PDF](200.37KB)
Cesaro summation by spheres of lattice sums and Madelung constants
Benjamin Galbally and Sergey Zelik
2021, 20(12) : 4195-4208 doi: 10.3934/cpaa.2021153 +[Abstract](237) +[HTML](113) +[PDF](483.09KB)
Uniform stability of the relativistic Cucker-Smale model and its application to a mean-field limit
Hyunjin Ahn, Seung-Yeal Ha and Jeongho Kim
2021, 20(12) : 4209-4237 doi: 10.3934/cpaa.2021156 +[Abstract](303) +[HTML](127) +[PDF](232.44KB)
Asymptotic expansion of the ground state energy for nonlinear Schrödinger system with three wave interaction
Kazuhiro Kurata and Yuki Osada
2021, 20(12) : 4239-4251 doi: 10.3934/cpaa.2021157 +[Abstract](272) +[HTML](106) +[PDF](153.51KB)
Periodic solutions for a class of second-order differential delay equations
Xuan Wu and Huafeng Xiao
2021, 20(12) : 4253-4269 doi: 10.3934/cpaa.2021159 +[Abstract](340) +[HTML](121) +[PDF](176.12KB)
Partial regularity result for non-autonomous elliptic systems with general growth
Teresa Isernia, Chiara Leone and Anna Verde
2021, 20(12) : 4271-4305 doi: 10.3934/cpaa.2021160 +[Abstract](267) +[HTML](118) +[PDF](271.77KB)
Local well-posedness for the Zakharov system in dimension $ d = 2, 3 $
Zijun Chen and Shengkun Wu
2021, 20(12) : 4307-4319 doi: 10.3934/cpaa.2021161 +[Abstract](270) +[HTML](127) +[PDF](229.53KB)
Time periodic solution to a two-species chemotaxis-Stokes system with $ p $-Laplacian diffusion
Chengxin Du and Changchun Liu
2021, 20(12) : 4321-4345 doi: 10.3934/cpaa.2021162 +[Abstract](427) +[HTML](170) +[PDF](469.72KB)
Semilinear Schrödinger evolution equations with inverse-square and harmonic potentials via pseudo-conformal symmetry
Toshiyuki Suzuki
2021, 20(12) : 4347-4377 doi: 10.3934/cpaa.2021163 +[Abstract](279) +[HTML](124) +[PDF](259.92KB)
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](516) +[HTML](285) +[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](682) +[HTML](338) +[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](626) +[HTML](265) +[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](496) +[HTML](286) +[PDF](782.03KB)
Hadamard Semidifferential, Oriented Distance Function, and some Applications
Michel C. Delfour
2021doi: 10.3934/cpaa.2021076 +[Abstract](614) +[HTML](285) +[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](603) +[HTML](362) +[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](608) +[HTML](270) +[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](506) +[HTML](330) +[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](426) +[HTML](229) +[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](396) +[HTML](176) +[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](339) +[HTML](225) +[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](427) +[HTML](218) +[PDF](488.08KB)
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](397) +[HTML](205) +[PDF](502.96KB)
Dynamical analysis in disease transmission and final epidemic size
Daifeng Duan, Cuiping Wang and Yuan Yuan
2021doi: 10.3934/cpaa.2021150 +[Abstract](285) +[HTML](128) +[PDF](961.2KB)
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](377) +[HTML](158) +[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](288) +[HTML](139) +[PDF](1835.77KB)
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](252) +[HTML](133) +[PDF](472.33KB)
Green's function for second order parabolic equations with singular lower order coefficients
Seick Kim and Longjuan Xu
2021doi: 10.3934/cpaa.2021164 +[Abstract](237) +[HTML](112) +[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](205) +[HTML](108) +[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](263) +[HTML](107) +[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](212) +[HTML](109) +[PDF](482.89KB)
Regularity and existence of positive solutions for a fractional system
Ran Zhuo and Yan Li
2021doi: 10.3934/cpaa.2021168 +[Abstract](218) +[HTML](111) +[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](305) +[HTML](112) +[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](197) +[HTML](183) +[PDF](2334.82KB)
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](217) +[HTML](99) +[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](212) +[HTML](105) +[PDF](437.55KB)
Marcinkiewicz integral operators along twisted surfaces
Ahmad Al-Salman
2021doi: 10.3934/cpaa.2021173 +[Abstract](236) +[HTML](107) +[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](159) +[HTML](66) +[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](221) +[HTML](76) +[PDF](538.49KB)
Variation operators for semigroups associated with Fourier-Bessel expansions
Jorge J. Betancor, Alejandro J. Castro and Marta De León-Contreras
2021doi: 10.3934/cpaa.2021176 +[Abstract](102) +[HTML](39) +[PDF](528.43KB)
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](141) +[HTML](83) +[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](172) +[HTML](118) +[PDF](606.92KB)
Dynamics of an SIRS epidemic model with cross-diffusion
Yaru Hu and Jinfeng Wang
2021doi: 10.3934/cpaa.2021179 +[Abstract](206) +[HTML](91) +[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](143) +[HTML](75) +[PDF](451.87KB)
A second-order accurate structure-preserving scheme for the Cahn-Hilliard equation with a dynamic boundary condition
Makoto Okumura, Takeshi Fukao, Daisuke Furihata and Shuji Yoshikawa
2021doi: 10.3934/cpaa.2021181 +[Abstract](167) +[HTML](70) +[PDF](1195.07KB)
A convergent finite difference method for computing minimal Lagrangian graphs
Brittany Froese Hamfeldt and Jacob Lesniewski
2021doi: 10.3934/cpaa.2021182 +[Abstract](103) +[HTML](38) +[PDF](2280.11KB)
Variation and oscillation for harmonic operators in the inverse Gaussian setting
Víctor Almeida and Jorge J. Betancor
2021doi: 10.3934/cpaa.2021183 +[Abstract](89) +[HTML](38) +[PDF](622.63KB)
Global well-posedness in a chemotaxis system with oxygen consumption
Xujie Yang
2021doi: 10.3934/cpaa.2021184 +[Abstract](130) +[HTML](60) +[PDF](456.55KB)
Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum
Xin Zhong
2021doi: 10.3934/cpaa.2021185 +[Abstract](145) +[HTML](65) +[PDF](442.17KB)
On a nonlinear Laplace equation related to the boundary Yamabe problem in the upper-half space
Gael Diebou Yomgne
2021doi: 10.3934/cpaa.2021186 +[Abstract](139) +[HTML](57) +[PDF](517.98KB)
Liouville type theorems for stable solutions of elliptic system involving the Grushin operator
Foued Mtiri
2021doi: 10.3934/cpaa.2021187 +[Abstract](135) +[HTML](56) +[PDF](365.88KB)
Wave breaking phenomena and global existence for the weakly dissipative generalized Camassa-Holm equation
Yonghui Zhou and Shuguan Ji
2021doi: 10.3934/cpaa.2021188 +[Abstract](158) +[HTML](62) +[PDF](142.76KB)
Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system in $ \mathbb{R}^3 $ nonlinear KGS system
Salah Missaoui
2021doi: 10.3934/cpaa.2021189 +[Abstract](81) +[HTML](32) +[PDF](169.48KB)
On a system of nonlinear pseudoparabolic equations with Robin-Dirichlet boundary conditions
Le Thi Phuong Ngoc, Khong Thi Thao Uyen, Nguyen Huu Nhan and Nguyen Thanh Long
2021doi: 10.3934/cpaa.2021190 +[Abstract](51) +[HTML](21) +[PDF](286.62KB)
Blowing-up solutions for a supercritical elliptic equation
Yessine Dammak
2021doi: 10.3934/cpaa.2021191 +[Abstract](94) +[HTML](37) +[PDF](165.96KB)
Synchronized and ground-state solutions to a coupled Schrödinger system
Mohammad Ali Husaini and Chuangye Liu
2021doi: 10.3934/cpaa.2021192 +[Abstract](131) +[HTML](47) +[PDF](243.28KB)
Multiple non-radially symmetrical nodal solutions for the Schrödinger system with positive quasilinear term
Jianqing Chen and Qian Zhang
2021doi: 10.3934/cpaa.2021193 +[Abstract](90) +[HTML](35) +[PDF](189.41KB)
Nonnegative solutions to a doubly degenerate nutrient taxis system
Genglin Li and Michael Winkler
2021doi: 10.3934/cpaa.2021194 +[Abstract](44) +[HTML](25) +[PDF](194.16KB)
Bifurcation, uniqueness and multiplicity results for classes of reaction diffusion equations arising in ecology with nonlinear boundary conditions
Mohan Mallick, Sarath Sasi, R. Shivaji and S. Sundar
2021doi: 10.3934/cpaa.2021195 +[Abstract](25) +[HTML](17) +[PDF](311.75KB)
Time analyticity of the biharmonic heat equation, the heat equation with potentials and some nonlinear heat equations
Chulan Zeng
2021doi: 10.3934/cpaa.2021197 +[Abstract](38) +[HTML](23) +[PDF](273.85KB)
A flow method for a generalization of $ L_{p} $ Christofell-Minkowski problem
Boya Li, Hongjie Ju and Yannan Liu
2021doi: 10.3934/cpaa.2021198 +[Abstract](28) +[HTML](14) +[PDF](142.06KB)
Asymptotic and quenching behaviors of semilinear parabolic systems with singular nonlinearities
Qi Wang and Yanyan Zhang
2021doi: 10.3934/cpaa.2021199 +[Abstract](31) +[HTML](19) +[PDF](218.45KB)
On regularity and stability for a class of nonlocal evolution equations with nonlinear perturbations
Dinh-Ke Tran and Nhu-Thang Nguyen
2021doi: 10.3934/cpaa.2021200 +[Abstract](57) +[HTML](18) +[PDF](169.47KB)
Radial symmetry of nonnegative solutions for nonlinear integral systems
Zhenjie Li and Chunqin Zhou
2021doi: 10.3934/cpaa.2021201 +[Abstract](27) +[HTML](11) +[PDF](118.6KB)
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](5940) +[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](3816) +[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](3993) +[HTML](243) +[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](5424) +[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](5136) +[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](3055) +[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](5077) +[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](3730) +[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](4342) +[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
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Bifurcation and stability of a two-species diffusive Lotka-Volterra model
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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](4777) +[PDF](486.1KB) PDF Downloads(811)
Mean value properties and unique continuation
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The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality
Apala Majumdar
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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](2834) +[HTML](109) +[PDF](356.11KB) PDF Downloads(577)
W1, p-estimates for elliptic equations with lower order terms
Byungsoo Kang and Hyunseok Kim
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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
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Nonlinear wave equation with both strongly and weakly damped terms: Supercritical initial energy finite time blow up
Yanbing Yang and Runzhang Xu
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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](1921) +[HTML](170) +[PDF](356.02KB) PDF Downloads(506)
Kirchhoff type equations with strong singularities
Yijing Sun and Yuxin Tan
2019, 18(1) : 181-193 doi: 10.3934/cpaa.2019010 +[Abstract](4505) +[HTML](216) +[PDF](342.2KB) PDF Downloads(491)

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5 Year Impact Factor: 1.510
2020 CiteScore: 1.9

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