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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.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 6 issues a year in January, March, May, July, September and November.
  • Publishes both online and in print.
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  • CPAA is issued jointly by the American Institute of Mathematical Sciences and Shanghai Jiao Tong University. All rights reserved.

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On the existence of solutions and causality for relativistic viscous conformal fluids
Marcelo M. Disconzi
2019, 18(4) : 1567-1599 doi: 10.3934/cpaa.2019075 +[Abstract](364) +[HTML](149) +[PDF](464.53KB)
The interior gradient estimate for some nonlinear curvature equations
Liangjun Weng
2019, 18(4) : 1601-1612 doi: 10.3934/cpaa.2019076 +[Abstract](362) +[HTML](146) +[PDF](296.92KB)
Effects of localized spatial variations on the uniform persistence and spreading speeds of time periodic two species competition systems
Liang Kong, Tung Nguyen and Wenxian Shen
2019, 18(4) : 1613-1636 doi: 10.3934/cpaa.2019077 +[Abstract](323) +[HTML](132) +[PDF](408.1KB)
New general decay results in a finite-memory bresse system
Salim A. Messaoudi and Jamilu Hashim Hassan
2019, 18(4) : 1637-1662 doi: 10.3934/cpaa.2019078 +[Abstract](332) +[HTML](148) +[PDF](392.82KB)
Ground state solutions for the fractional Schrödinger-Poisson systems involving critical growth in $ \mathbb{R} ^{3} $
Lun Guo, Wentao Huang and Huifang Jia
2019, 18(4) : 1663-1693 doi: 10.3934/cpaa.2019079 +[Abstract](336) +[HTML](146) +[PDF](475.74KB)
Multiple solutions for periodic perturbations of a delayed autonomous system near an equilibrium
Pablo Amster, Mariel Paula Kuna and Gonzalo Robledo
2019, 18(4) : 1695-1709 doi: 10.3934/cpaa.2019080 +[Abstract](258) +[HTML](114) +[PDF](363.52KB)
Scattering results for Dirac Hartree-type equations with small initial data
Changhun Yang
2019, 18(4) : 1711-1734 doi: 10.3934/cpaa.2019081 +[Abstract](266) +[HTML](125) +[PDF](412.87KB)
Remarks on a system of quasi-linear wave equations in 3D satisfying the weak null condition
Kunio Hidano and Dongbing Zha
2019, 18(4) : 1735-1767 doi: 10.3934/cpaa.2019082 +[Abstract](249) +[HTML](117) +[PDF](467.74KB)
Global existence for the Boltzmann equation in $ L^r_v L^\infty_t L^\infty_x $ spaces
Koya Nishimura
2019, 18(4) : 1769-1782 doi: 10.3934/cpaa.2019083 +[Abstract](320) +[HTML](119) +[PDF](348.94KB)
Existence and regularity of solutions for an evolution model of perfectly plastic plates
P. Gidoni, G. B. Maggiani and R. Scala
2019, 18(4) : 1783-1826 doi: 10.3934/cpaa.2019084 +[Abstract](224) +[HTML](119) +[PDF](479.94KB)
Second order non-autonomous lattice systems and their uniform attractors
Ahmed Y. Abdallah and Rania T. Wannan
2019, 18(4) : 1827-1846 doi: 10.3934/cpaa.2019085 +[Abstract](237) +[HTML](114) +[PDF](388.29KB)
Nonlinear Dirichlet problem for the nonlocal anisotropic operator $ L_K $
Silvia Frassu
2019, 18(4) : 1847-1867 doi: 10.3934/cpaa.2019086 +[Abstract](253) +[HTML](117) +[PDF](392.09KB)
Global attractors for a mixture problem in one dimensional solids with nonlinear damping and sources terms
M. L. Santos and Mirelson M. Freitas
2019, 18(4) : 1869-1890 doi: 10.3934/cpaa.2019087 +[Abstract](517) +[HTML](130) +[PDF](380.3KB)
Well-posedness of low regularity solutions to the second order strictly hyperbolic equations with non-Lipschitzian coefficients
Wenming Hu and Huicheng Yin
2019, 18(4) : 1891-1919 doi: 10.3934/cpaa.2019088 +[Abstract](240) +[HTML](146) +[PDF](453.0KB)
Spike layer solutions for a singularly perturbed Neumann problem: Variational construction without a nondegeneracy
Jaeyoung Byeon and Sang-hyuck Moon
2019, 18(4) : 1921-1965 doi: 10.3934/cpaa.2019089 +[Abstract](264) +[HTML](124) +[PDF](523.48KB)
$ L^p $-$ L^q $ estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data
Masahiro Ikeda, Takahisa Inui, Mamoru Okamoto and Yuta Wakasugi
2019, 18(4) : 1967-2008 doi: 10.3934/cpaa.2019090 +[Abstract](286) +[HTML](122) +[PDF](544.49KB)
Existence, multiplicity and concentration for a class of fractional $ p \& q $ Laplacian problems in $ \mathbb{R} ^{N} $
Claudianor O. Alves, Vincenzo Ambrosio and Teresa Isernia
2019, 18(4) : 2009-2045 doi: 10.3934/cpaa.2019091 +[Abstract](295) +[HTML](191) +[PDF](511.84KB)
A chemotaxis-haptotaxis system with haptoattractant remodeling: Boundedness enforced by mild saturation of signal production
Youshan Tao and Michael Winkler
2019, 18(4) : 2047-2067 doi: 10.3934/cpaa.2019092 +[Abstract](296) +[HTML](130) +[PDF](386.29KB)
Multidimensional stability of planar traveling waves for the delayed nonlocal dispersal competitive Lotka-Volterra system
Zhaohai Ma, Rong Yuan, Yang Wang and Xin Wu
2019, 18(4) : 2069-2092 doi: 10.3934/cpaa.2019093 +[Abstract](299) +[HTML](132) +[PDF](519.32KB)
On stability properties of the Cubic-Quintic Schródinger equation with $\delta$-point interaction
Jaime Angulo Pava and César A. Hernández Melo
2019, 18(4) : 2093-2116 doi: 10.3934/cpaa.2019094 +[Abstract](286) +[HTML](124) +[PDF](468.08KB)
On a formula for sets of constant width in 2d
Bernd Kawohl and Guido Sweers
2019, 18(4) : 2117-2131 doi: 10.3934/cpaa.2019095 +[Abstract](351) +[HTML](151) +[PDF](637.45KB)
Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids
Zhenhua Guo, Wenchao Dong and Jinjing Liu
2019, 18(4) : 2133-2161 doi: 10.3934/cpaa.2019096 +[Abstract](265) +[HTML](122) +[PDF](399.92KB)
Word combinatorics for stochastic differential equations: Splitting integrators
A. Alamo and J. M. Sanz-Serna
2019, 18(4) : 2163-2195 doi: 10.3934/cpaa.2019097 +[Abstract](264) +[HTML](138) +[PDF](465.98KB)
Corrigendum to the paper: Nonuniqueness in Vector-Valued Calculus of Variations in $ L^\infty $ and some Linear Elliptic Systems
Nikos Katzourakis
2019, 18(4) : 2197-2198 doi: 10.3934/cpaa.2019098 +[Abstract](244) +[HTML](129) +[PDF](221.02KB)
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](2211) +[PDF](826.7KB) Cited By(58)
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](1942) +[PDF](509.5KB) Cited By(57)
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](1514) +[PDF](102.3KB) Cited By(57)
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](1552) +[PDF](181.7KB) Cited By(56)
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](1391) +[PDF](395.6KB) Cited By(46)
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](1816) +[PDF](1276.3KB) Cited By(42)
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](1492) +[PDF](318.8KB) Cited By(42)
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](1362) +[PDF](113.6KB) Cited By(42)
Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent
Sergey Zelik
2004, 3(4) : 921-934 doi: 10.3934/cpaa.2004.3.921 +[Abstract](1576) +[PDF](176.4KB) Cited By(39)
Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights
M. Chuaqui, C. Cortázar, M. Elgueta and J. García-Melián
2004, 3(4) : 653-662 doi: 10.3934/cpaa.2004.3.653 +[Abstract](1452) +[PDF](152.5KB) Cited By(39)
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](1840) +[HTML](396) +[PDF](462.14KB) PDF Downloads(207)
The Nehari manifold for a fractional Laplacian equation involving critical nonlinearities
Qingfang Wang
2018, 17(6) : 2261-2281 doi: 10.3934/cpaa.2018108 +[Abstract](1404) +[HTML](147) +[PDF](409.64KB) PDF Downloads(152)
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](644) +[HTML](208) +[PDF](382.99KB) PDF Downloads(143)
Multiplicity and concentration of positive solutions for fractional nonlinear Schrödinger equation
Xudong Shang and Jihui Zhang
2018, 17(6) : 2239-2259 doi: 10.3934/cpaa.2018107 +[Abstract](1198) +[HTML](147) +[PDF](391.77KB) PDF Downloads(137)
\begin{document}$\mathbb{R}^3$\end{document}" >Space-time decay estimates of solutions to liquid crystal system in $\mathbb{R}^3$
Xiaopeng Zhao
2019, 18(1) : 1-13 doi: 10.3934/cpaa.2019001 +[Abstract](923) +[HTML](149) +[PDF](332.85KB) PDF Downloads(136)
Large time behavior of solutions of local and nonlocal nondegenerate Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator
Thi Tuyen Nguyen
2019, 18(3) : 999-1021 doi: 10.3934/cpaa.2019049 +[Abstract](653) +[HTML](190) +[PDF](411.33KB) PDF Downloads(133)
Symmetry and asymptotic behavior of ground state solutions for schrödinger systems with linear interaction
Zhitao Zhang and Haijun Luo
2018, 17(3) : 787-806 doi: 10.3934/cpaa.2018040 +[Abstract](1604) +[HTML](358) +[PDF](480.5KB) PDF Downloads(130)
\begin{document}$ \phi $\end{document}-Laplacian equations with mixed nonlinearities" >Homoclinic solutions of discrete $ \phi $-Laplacian equations with mixed nonlinearities
Genghong Lin and Zhan Zhou
2018, 17(5) : 1723-1747 doi: 10.3934/cpaa.2018082 +[Abstract](1233) +[HTML](230) +[PDF](490.86KB) PDF Downloads(126)
Existence results for linear evolution equations of parabolic type
Tôn Việt Tạ
2018, 17(3) : 751-785 doi: 10.3934/cpaa.2018039 +[Abstract](1478) +[HTML](377) +[PDF](504.53KB) PDF Downloads(124)
A loop type component in the non-negative solutions set of an indefinite elliptic problem
Humberto Ramos Quoirin and Kenichiro Umezu
2018, 17(3) : 1255-1269 doi: 10.3934/cpaa.2018060 +[Abstract](1333) +[HTML](341) +[PDF](417.1KB) PDF Downloads(124)

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