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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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Ground state solutions for fractional scalar field equations under a general critical nonlinearity
Claudianor O. Alves, Giovany M. Figueiredo and Gaetano Siciliano
2019, 18(5) : 2199-2215 doi: 10.3934/cpaa.2019099 +[Abstract](165) +[HTML](99) +[PDF](376.28KB)
On three-wave interaction Schrödinger systems with quadratic nonlinearities: Global well-posedness and standing waves
Ademir Pastor
2019, 18(5) : 2217-2242 doi: 10.3934/cpaa.2019100 +[Abstract](155) +[HTML](102) +[PDF](416.6KB)
On the existence and uniqueness of solution to a stochastic simplified liquid crystal model
T. Tachim Medjo
2019, 18(5) : 2243-2264 doi: 10.3934/cpaa.2019101 +[Abstract](157) +[HTML](116) +[PDF](472.24KB)
Uniqueness and radial symmetry of minimizers for a nonlocal variational problem
Orlando Lopes
2019, 18(5) : 2265-2282 doi: 10.3934/cpaa.2019102 +[Abstract](139) +[HTML](89) +[PDF](336.54KB)
Global attractor of the Cahn-Hilliard-Navier-Stokes system with moving contact lines
Bo You
2019, 18(5) : 2283-2298 doi: 10.3934/cpaa.2019103 +[Abstract](153) +[HTML](145) +[PDF](338.53KB)
Ground state solutions for asymptotically periodic modified Schr$ \ddot{\mbox{o}} $dinger-Poisson system involving critical exponent
Yong-Yong Li, Yan-Fang Xue and Chun-Lei Tang
2019, 18(5) : 2299-2324 doi: 10.3934/cpaa.2019104 +[Abstract](167) +[HTML](94) +[PDF](441.36KB)
Stability and asymptotic profile of steady state solutions to a reaction-diffusion pelagic-benthic algae growth model
Junping Shi, Jimin Zhang and Xiaoyan Zhang
2019, 18(5) : 2325-2347 doi: 10.3934/cpaa.2019105 +[Abstract](164) +[HTML](114) +[PDF](390.1KB)
Random attractor for the 2D stochastic nematic liquid crystals flows
Boling Guo, Yongqian Han and Guoli Zhou
2019, 18(5) : 2349-2376 doi: 10.3934/cpaa.2019106 +[Abstract](137) +[HTML](110) +[PDF](420.36KB)
Molecular characterization of anisotropic weak Musielak-Orlicz Hardy spaces and their applications
Ruirui Sun, Jinxia Li and Baode Li
2019, 18(5) : 2377-2395 doi: 10.3934/cpaa.2019107 +[Abstract](127) +[HTML](109) +[PDF](424.11KB)
Refined regularity for the blow-up set at non characteristic points for the vector-valued semilinear wave equation
Asma Azaiez
2019, 18(5) : 2397-2408 doi: 10.3934/cpaa.2019108 +[Abstract](141) +[HTML](91) +[PDF](346.85KB)
Dynamics of non-autonomous fractional stochastic Ginzburg-Landau equations with multiplicative noise
Yun Lan and Ji Shu
2019, 18(5) : 2409-2431 doi: 10.3934/cpaa.2019109 +[Abstract](145) +[HTML](96) +[PDF](406.19KB)
Existence and decay property of ground state solutions for Hamiltonian elliptic system
Jian Zhang and Wen Zhang
2019, 18(5) : 2433-2455 doi: 10.3934/cpaa.2019110 +[Abstract](100) +[HTML](81) +[PDF](407.56KB)
Global asymptotic stability of traveling waves to the Allen-Cahn equation with a fractional Laplacian
Luyi Ma, Hong-Tao Niu and Zhi-Cheng Wang
2019, 18(5) : 2457-2472 doi: 10.3934/cpaa.2019111 +[Abstract](97) +[HTML](69) +[PDF](331.91KB)
A note on global existence for the Zakharov system on $ \mathbb{T} $
E. Compaan
2019, 18(5) : 2473-2489 doi: 10.3934/cpaa.2019112 +[Abstract](86) +[HTML](54) +[PDF](403.55KB)
Large deviations for stochastic 3D Leray-$ \alpha $ model with fractional dissipation
Shihu Li, Wei Liu and Yingchao Xie
2019, 18(5) : 2491-2509 doi: 10.3934/cpaa.2019113 +[Abstract](131) +[HTML](80) +[PDF](488.97KB)
Effects of dispersal for a predator-prey model in a heterogeneous environment
Yaying Dong, Shanbing Li and Yanling Li
2019, 18(5) : 2511-2528 doi: 10.3934/cpaa.2019114 +[Abstract](88) +[HTML](64) +[PDF](350.23KB)
Global existence and asymptotic behavior of spherically symmetric solutions for the multi-dimensional infrarelativistic model
Yuming Qin and Jianlin Zhang
2019, 18(5) : 2529-2574 doi: 10.3934/cpaa.2019115 +[Abstract](97) +[HTML](66) +[PDF](479.45KB)
On extension problem, trace Hardy and Hardy's inequalities for some fractional Laplacians
Pradeep Boggarapu, Luz Roncal and Sundaram Thangavelu
2019, 18(5) : 2575-2605 doi: 10.3934/cpaa.2019116 +[Abstract](91) +[HTML](59) +[PDF](559.14KB)
Local well-posedness of the fifth-order KdV-type equations on the half-line
Márcio Cavalcante and Chulkwang Kwak
2019, 18(5) : 2607-2661 doi: 10.3934/cpaa.2019117 +[Abstract](93) +[HTML](55) +[PDF](621.02KB)
Qualitative properties of stationary solutions of the NLS on the Hyperbolic space without and with external potentials
Alessandro Selvitella
2019, 18(5) : 2663-2677 doi: 10.3934/cpaa.2019118 +[Abstract](85) +[HTML](48) +[PDF](340.08KB)
Faber-Krahn and Lieb-type inequalities for the composite membrane problem
Giovanni Cupini and Eugenio Vecchi
2019, 18(5) : 2679-2691 doi: 10.3934/cpaa.2019119 +[Abstract](48) +[HTML](33) +[PDF](360.91KB)
Concentration of ground state solutions for quasilinear Schrödinger systems with critical exponents
Yongpeng Chen, Yuxia Guo and Zhongwei Tang
2019, 18(5) : 2693-2715 doi: 10.3934/cpaa.2019120 +[Abstract](108) +[HTML](91) +[PDF](477.94KB)
Singular Hardy-Trudinger-Moser inequality and the existence of extremals on the unit disc
Xumin Wang
2019, 18(5) : 2717-2733 doi: 10.3934/cpaa.2019121 +[Abstract](90) +[HTML](72) +[PDF](455.9KB)
Scattering in the weighted $ L^2 $-space for a 2D nonlinear Schrödinger equation with inhomogeneous exponential nonlinearity
Abdelwahab Bensouilah, Van Duong Dinh and Mohamed Majdoub
2019, 18(5) : 2735-2755 doi: 10.3934/cpaa.2019122 +[Abstract](121) +[HTML](54) +[PDF](510.23KB)
Higher order conformally invariant equations in $ {\mathbb R}^3 $ with prescribed volume
Ali Hyder and Juncheng Wei
2019, 18(5) : 2757-2764 doi: 10.3934/cpaa.2019123 +[Abstract](93) +[HTML](82) +[PDF](367.08KB)
Existence, uniqueness and regularity of the solution of the time-fractional Fokker–Planck equation with general forcing
Kim-Ngan Le, William McLean and Martin Stynes
2019, 18(5) : 2765-2787 doi: 10.3934/cpaa.2019124 +[Abstract](99) +[HTML](51) +[PDF](507.76KB)
Optimal indirect stability of a weakly damped elastic abstract system of second order equations coupled by velocities
Farah Abdallah, Mouhammad Ghader, Ali Wehbe and Yacine Chitour
2019, 18(5) : 2789-2818 doi: 10.3934/cpaa.2019125 +[Abstract](102) +[HTML](55) +[PDF](551.24KB)
A symmetry result for elliptic systems in punctured domains
Stefano Biagi, Enrico Valdinoci and Eugenio Vecchi
2019, 18(5) : 2819-2833 doi: 10.3934/cpaa.2019126 +[Abstract](80) +[HTML](66) +[PDF](375.22KB)
Pointwise estimates of solutions to conservation laws with nonlocal dissipation-type terms
Lijuan Wang and Weike Wang
2019, 18(5) : 2835-2854 doi: 10.3934/cpaa.2019127 +[Abstract](90) +[HTML](83) +[PDF](449.54KB)
Homoclinic orbits for a class of asymptotically quadratic Hamiltonian systems
Ying Lv, Yan-Fang Xue and Chun-Lei Tang
2019, 18(5) : 2855-2878 doi: 10.3934/cpaa.2019128 +[Abstract](60) +[HTML](37) +[PDF](493.95KB)
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](2374) +[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](2095) +[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](1646) +[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](1686) +[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](1511) +[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](1956) +[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](1616) +[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](1471) +[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](1718) +[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](1584) +[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](1969) +[HTML](396) +[PDF](462.14KB) PDF Downloads(210)
The Nehari manifold for a fractional Laplacian equation involving critical nonlinearities
Qingfang Wang
2018, 17(6) : 2261-2281 doi: 10.3934/cpaa.2018108 +[Abstract](1609) +[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](802) +[HTML](209) +[PDF](382.99KB) PDF Downloads(144)
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](1384) +[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](1069) +[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](819) +[HTML](190) +[PDF](411.33KB) PDF Downloads(134)
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](1749) +[HTML](359) +[PDF](480.5KB) PDF Downloads(132)
\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](1373) +[HTML](231) +[PDF](490.86KB) PDF Downloads(128)
Existence results for linear evolution equations of parabolic type
Tôn Việt Tạ
2018, 17(3) : 751-785 doi: 10.3934/cpaa.2018039 +[Abstract](1586) +[HTML](377) +[PDF](504.53KB) PDF Downloads(125)
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](1460) +[HTML](341) +[PDF](417.1KB) PDF Downloads(124)

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