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CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal's highest standard and closest link to the scientific communities.


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A convergent Lagrangian discretization for $ p $-Wasserstein and flux-limited diffusion equations
Benjamin Söliver and Oliver Junge
2020, 19(9) : 4227-4256 doi: 10.3934/cpaa.2020190 +[Abstract](103) +[HTML](58) +[PDF](1370.19KB)
On nonexistence of extremals for the Trudinger-Moser functionals involving $ L^p $ norms
Yamin Wang
2020, 19(9) : 4257-4268 doi: 10.3934/cpaa.2020191 +[Abstract](88) +[HTML](35) +[PDF](443.58KB)
Existence of infinitely many solutions for semilinear problems on exterior domains
Joseph Iaia
2020, 19(9) : 4269-4284 doi: 10.3934/cpaa.2020193 +[Abstract](85) +[HTML](40) +[PDF](426.4KB)
On special regularity properties of solutions of the benjamin-ono-zakharov-kuznetsov (bo-zk) equation
A. C. Nascimento
2020, 19(9) : 4285-4325 doi: 10.3934/cpaa.2020194 +[Abstract](120) +[HTML](44) +[PDF](667.8KB)
Existence of monotone positive solutions of a neighbour based chemotaxis model and aggregation phenomenon
Xin Xu
2020, 19(9) : 4327-4348 doi: 10.3934/cpaa.2020195 +[Abstract](102) +[HTML](44) +[PDF](501.3KB)
Asymptotic behavior of solutions for nonlinear integral equations with Hénon type on the unit Ball
Ziyi Cai and Haiyang He
2020, 19(9) : 4349-4362 doi: 10.3934/cpaa.2020196 +[Abstract](88) +[HTML](47) +[PDF](412.52KB)
Monotonicity with respect to $ p $ of the First Nontrivial Eigenvalue of the $ p $-Laplacian with Homogeneous Neumann Boundary Conditions
Mihai Mihăilescu and Julio D. Rossi
2020, 19(9) : 4363-4371 doi: 10.3934/cpaa.2020198 +[Abstract](82) +[HTML](45) +[PDF](356.81KB)
Large time behavior of ODE type solutions to parabolic $ p $-Laplacian type equations
Junyong Eom and Ryuichi Sato
2020, 19(9) : 4373-4386 doi: 10.3934/cpaa.2020199 +[Abstract](82) +[HTML](35) +[PDF](408.29KB)
Maximum principles for a fully nonlinear nonlocal equation on unbounded domains
Xiaoming He, Xin Zhao and Wenming Zou
2020, 19(9) : 4387-4399 doi: 10.3934/cpaa.2020200 +[Abstract](102) +[HTML](38) +[PDF](400.81KB)
Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials
Marcos L. M. Carvalho, Edcarlos D. Silva, Claudiney Goulart and Carlos A. Santos
2020, 19(9) : 4401-4432 doi: 10.3934/cpaa.2020201 +[Abstract](103) +[HTML](50) +[PDF](559.92KB)
A second order fractional differential equation under effects of a super damping
Ruy Coimbra Charão, Juan Torres Espinoza and Ryo Ikehata
2020, 19(9) : 4433-4454 doi: 10.3934/cpaa.2020202 +[Abstract](88) +[HTML](41) +[PDF](470.3KB)
Improved blow up criterion for the three dimensional incompressible magnetohydrodynamics system
Bin Han and Na Zhao
2020, 19(9) : 4455-4478 doi: 10.3934/cpaa.2020203 +[Abstract](89) +[HTML](38) +[PDF](454.5KB)
Exponential mixing for the fractional Magneto-Hydrodynamic equations with degenerate stochastic forcing
Xuhui Peng, Jianhua Huang and Yan Zheng
2020, 19(9) : 4479-4506 doi: 10.3934/cpaa.2020204 +[Abstract](67) +[HTML](51) +[PDF](554.4KB)
Motion of interfaces for a damped hyperbolic Allen–Cahn equation
Raffaele Folino, Corrado Lattanzio and Corrado Mascia
2020, 19(9) : 4507-4543 doi: 10.3934/cpaa.2020205 +[Abstract](106) +[HTML](43) +[PDF](746.53KB)
Finite dimensional global attractor for a damped fractional anisotropic Schrödinger type equation with harmonic potential
Brahim Alouini
2020, 19(9) : 4545-4573 doi: 10.3934/cpaa.2020206 +[Abstract](78) +[HTML](44) +[PDF](623.52KB)
Optimal decay to the non-isentropic compressible micropolar fluids
Lvqiao liu and Lan Zhang
2020, 19(9) : 4575-4598 doi: 10.3934/cpaa.2020207 +[Abstract](76) +[HTML](47) +[PDF](505.7KB)
The effect of nonlocal reaction in an epidemic model with nonlocal diffusion and free boundaries
Meng Zhao, Wantong Li and Yihong Du
2020, 19(9) : 4599-4620 doi: 10.3934/cpaa.2020208 +[Abstract](93) +[HTML](44) +[PDF](487.32KB)
Fast and slow velocity alignments in a Cucker-Smale ensemble with adaptive couplings
Seung-Yeal Ha, Dohyun Kim and Jinyeong Park
2020, 19(9) : 4621-4654 doi: 10.3934/cpaa.2020209 +[Abstract](102) +[HTML](50) +[PDF](1695.08KB)
Existence and nonexistence of positive radial solutions for a class of $p$-Laplacian superlinear problems with nonlinear boundary conditions
Trad Alotaibi, D. D. Hai and R. Shivaji
2020, 19(9) : 4655-4666 doi: 10.3934/cpaa.2020131 +[Abstract](98) +[HTML](35) +[PDF](371.78KB)
Degenerate coercive quasilinear elliptic equations with subcritical or critical exponents in $ \mathbb{R}^N $
Yaotian Shen and Youjun Wang
2020, 19(9) : 4667-4697 doi: 10.3934/cpaa.2020197 +[Abstract](79) +[HTML](41) +[PDF](547.35KB)
Hardy inequalities for the fractional powers of the Grushin operator
Manli Song and Jinggang Tan
2020, 19(9) : 4699-4726 doi: 10.3934/cpaa.2020192 +[Abstract](99) +[HTML](39) +[PDF](540.99KB)
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](4171) +[PDF](826.7KB) Cited By(98)
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](3236) +[PDF](181.7KB) Cited By(87)
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](3819) +[PDF](509.5KB) Cited By(83)
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](1814) +[HTML](222) +[PDF](373.99KB) Cited By(70)
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](3076) +[PDF](102.3KB) Cited By(67)
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](2889) +[PDF](395.6KB) Cited By(63)
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](3528) +[PDF](1276.3KB) Cited By(61)
Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval
Shou-Fu Tian
2018, 17(3) : 923-957 doi: 10.3934/cpaa.2018046 +[Abstract](41980) +[HTML](386) +[PDF](546.2KB) Cited By(55)
Global weak solutions for a viscous liquid-gas model with singular pressure law
Steinar Evje and Kenneth Hvistendahl Karlsen
2009, 8(6) : 1867-1894 doi: 10.3934/cpaa.2009.8.1867 +[Abstract](2917) +[PDF](318.8KB) Cited By(49)
A result on the existence of global attractors for semigroups of closed operators
V. Pata and Sergey Zelik
2007, 6(2) : 481-486 doi: 10.3934/cpaa.2007.6.481 +[Abstract](2753) +[PDF](113.6KB) Cited By(47)
Semi-exact solutions and pulsating fronts for Lotka-Volterra systems of two competing species in spatially periodic habitats
Chiun-Chuan Chen, Yin-Liang Huang, Li-Chang Hung and Chang-Hong Wu
2020, 19(1) : 1-18 doi: 10.3934/cpaa.2020001 +[Abstract](1398) +[HTML](251) +[PDF](460.49KB) PDF Downloads(278)
Random attractors for stochastic parabolic equations with additive noise in weighted spaces
Xiaojun Li, Xiliang Li and Kening Lu
2018, 17(3) : 729-749 doi: 10.3934/cpaa.2018038 +[Abstract](4950) +[HTML](492) +[PDF](462.14KB) PDF Downloads(278)
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](2934) +[PDF](486.1KB) PDF Downloads(266)
Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity
Mohammad M. Al-Gharabli, Aissa Guesmia and Salim A. Messaoudi
2019, 18(1) : 159-180 doi: 10.3934/cpaa.2019009 +[Abstract](4126) +[HTML](246) +[PDF](367.7KB) PDF Downloads(261)
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](3805) +[HTML](213) +[PDF](328.43KB) PDF Downloads(261)
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](3273) +[HTML](349) +[PDF](342.33KB) PDF Downloads(258)
The properties of positive solutions to semilinear equations involving the fractional Laplacian
Rongrong Yang and Zhongxue Lü
2019, 18(3) : 1073-1089 doi: 10.3934/cpaa.2019052 +[Abstract](3541) +[HTML](316) +[PDF](382.99KB) PDF Downloads(249)
The Nehari manifold for a fractional Laplacian equation involving critical nonlinearities
Qingfang Wang
2018, 17(6) : 2261-2281 doi: 10.3934/cpaa.2018108 +[Abstract](4661) +[HTML](258) +[PDF](409.64KB) PDF Downloads(225)
Spreading speeds and traveling waves for space-time periodic nonlocal dispersal cooperative systems
Xiongxiong Bao, Wenxian Shen and Zhongwei Shen
2019, 18(1) : 361-396 doi: 10.3934/cpaa.2019019 +[Abstract](3967) +[HTML](225) +[PDF](502.44KB) PDF Downloads(223)
Ground states of nonlinear fractional Choquard equations with Hardy-Littlewood-Sobolev critical growth
Hua Jin, Wenbin Liu, Huixing Zhang and Jianjun Zhang
2020, 19(1) : 123-144 doi: 10.3934/cpaa.2020008 +[Abstract](1273) +[HTML](251) +[PDF](380.39KB) PDF Downloads(221)

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