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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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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](476) +[HTML](154) +[PDF](460.49KB)
Entire subsolutions of Monge-Ampère type equations
Limei Dai and Hongyu Li
2020, 19(1) : 19-30 doi: 10.3934/cpaa.2020002 +[Abstract](375) +[HTML](129) +[PDF](334.0KB)
Infinitely many solutions and Morse index for non-autonomous elliptic problems
Philip Korman
2020, 19(1) : 31-46 doi: 10.3934/cpaa.2020003 +[Abstract](437) +[HTML](139) +[PDF](342.49KB)
Analysis on hybrid fractals
P. Alonso Ruiz, Y. Chen, H. Gu, R. S. Strichartz and Z. Zhou
2020, 19(1) : 47-84 doi: 10.3934/cpaa.2020004 +[Abstract](366) +[HTML](136) +[PDF](2207.32KB)
Dynamics of spatially heterogeneous viral model with time delay
Hong Yang and Junjie Wei
2020, 19(1) : 85-102 doi: 10.3934/cpaa.2020005 +[Abstract](366) +[HTML](136) +[PDF](342.62KB)
Remarks on singular trudinger-moser type inequalities
Xiaobao Zhu
2020, 19(1) : 103-112 doi: 10.3934/cpaa.2020006 +[Abstract](285) +[HTML](153) +[PDF](354.23KB)
Estimates for sums of eigenvalues of the free plate via the fourier transform
Barbara Brandolini, Francesco Chiacchio and Jeffrey J. Langford
2020, 19(1) : 113-122 doi: 10.3934/cpaa.2020007 +[Abstract](252) +[HTML](133) +[PDF](294.87KB)
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](305) +[HTML](160) +[PDF](380.39KB)
Local integral manifolds for nonautonomous and ill-posed equations with sectorially dichotomous operator
Lianwang Deng
2020, 19(1) : 145-174 doi: 10.3934/cpaa.2020009 +[Abstract](277) +[HTML](120) +[PDF](454.4KB)
Droplet phase in a nonlocal isoperimetric problem under confinement
Stan Alama, Lia Bronsard, Rustum Choksi and Ihsan Topaloglu
2020, 19(1) : 175-202 doi: 10.3934/cpaa.2020010 +[Abstract](243) +[HTML](138) +[PDF](626.84KB)
The continuous morbidostat: A chemostat with controlled drug application to select for drug resistance mutants
Zhenzhen Chen, Sze-Bi Hsu and Ya-Tang Yang
2020, 19(1) : 203-220 doi: 10.3934/cpaa.2020011 +[Abstract](293) +[HTML](147) +[PDF](1271.49KB)
Multiplicity of positive solutions to nonlinear systems of Hammerstein integral equations with weighted functions
Xiyou Cheng, Zhaosheng Feng and Zhitao Zhang
2020, 19(1) : 221-240 doi: 10.3934/cpaa.2020012 +[Abstract](325) +[HTML](121) +[PDF](359.15KB)
Positive solutions for the one-dimensional singular superlinear $ p $-Laplacian problem
K. D. Chu and D. D. Hai
2020, 19(1) : 241-252 doi: 10.3934/cpaa.2020013 +[Abstract](289) +[HTML](134) +[PDF](350.92KB)
Uniqueness and stability of time-periodic pyramidal fronts for a periodic competition-diffusion system
Xiongxiong Bao, Wan-Tong Li and Zhi-Cheng Wang
2020, 19(1) : 253-277 doi: 10.3934/cpaa.2020014 +[Abstract](273) +[HTML](139) +[PDF](441.36KB)
Infinitely many subharmonic solutions for nonlinear equations with singular $ \phi $-Laplacian
Xiying Sun, Qihuai Liu, Dingbian Qian and Na Zhao
2020, 19(1) : 279-292 doi: 10.3934/cpaa.20200015 +[Abstract](249) +[HTML](125) +[PDF](372.06KB)
Averaging principles for the Swift-Hohenberg equation
Peng Gao
2020, 19(1) : 293-310 doi: 10.3934/cpaa.2020016 +[Abstract](262) +[HTML](130) +[PDF](350.19KB)
Multi-spikes solutions for a system of coupled elliptic equations with quadratic nonlinearity
Zhongwei Tang and Huafei Xie
2020, 19(1) : 311-328 doi: 10.3934/cpaa.2020017 +[Abstract](234) +[HTML](147) +[PDF](372.85KB)
Least energy solutions for coupled hartree system with hardy-littlewood-sobolev critical exponents
Yu Zheng, Carlos A. Santos, Zifei Shen and Minbo Yang
2020, 19(1) : 329-369 doi: 10.3934/cpaa.2020018 +[Abstract](277) +[HTML](156) +[PDF](528.38KB)
Generalized transforms and generalized convolution products associated with Gaussian paths on function space
Seung Jun Chang and Jae Gil Choi
2020, 19(1) : 371-389 doi: 10.3934/cpaa.2020019 +[Abstract](246) +[HTML](126) +[PDF](384.11KB)
Existence and multiplicity of nontrivial solutions of biharmonic equations via differential inclusion
Ziqing Yuana and Jianshe Yu
2020, 19(1) : 391-405 doi: 10.3934/cpaa.2020020 +[Abstract](266) +[HTML](125) +[PDF](354.53KB)
Analytic integrability around a nilpotent singularity: The non-generic case
Antonio Algaba, María Díaz, Cristóbal García and Jaume Giné
2020, 19(1) : 407-423 doi: 10.3934/cpaa.2020021 +[Abstract](236) +[HTML](115) +[PDF](371.21KB)
On the Schrödinger-Debye system in compact Riemannian manifolds
Marcelo Nogueira and Mahendra Panthee
2020, 19(1) : 425-453 doi: 10.3934/cpaa.2020022 +[Abstract](261) +[HTML](160) +[PDF](461.52KB)
Existence, blow-up and exponential decay estimates for a system of nonlinear viscoelastic wave equations with nonlinear boundary conditions
Nguyen Thanh Long, Hoang Hai Ha, Le Thi Phuong Ngoc and Nguyen Anh Triet
2020, 19(1) : 455-492 doi: 10.3934/cpaa.2020023 +[Abstract](307) +[HTML](146) +[PDF](477.95KB)
The weak maximum principle for second-order elliptic and parabolic conormal derivative problems
Doyoon Kim and Seungjin Ryu
2020, 19(1) : 493-510 doi: 10.3934/cpaa.2020024 +[Abstract](268) +[HTML](141) +[PDF](369.86KB)
Liouville theorems for stable weak solutions of elliptic problems involving Grushin operator
Phuong Le
2020, 19(1) : 511-525 doi: 10.3934/cpaa.2020025 +[Abstract](301) +[HTML](131) +[PDF](360.61KB)
Symmetry of singular solutions for a weighted Choquard equation involving the fractional $ p $-Laplacian
Phuong Le
2020, 19(1) : 527-539 doi: 10.3934/cpaa.2020026 +[Abstract](341) +[HTML](131) +[PDF](341.52KB)
Almost-periodic perturbations of non-hyperbolic equilibrium points via Pöschel-Rüssmann KAM method
Wen Si, Fenfen Wang and Jianguo Si
2020, 19(1) : 541-585 doi: 10.3934/cpaa.2020027 +[Abstract](229) +[HTML](128) +[PDF](556.25KB)
Potential well and multiplicity of solutions for nonlinear Dirac equations
Yu Chen, Yanheng Ding and Tian Xu
2020, 19(1) : 587-607 doi: 10.3934/cpaa.2020028 +[Abstract](287) +[HTML](170) +[PDF](419.77KB)
On large potential perturbations of the Schrödinger, wave and Klein–Gordon equations
P. D'Ancona
2020, 19(1) : 609-640 doi: 10.3934/cpaa.2020029 +[Abstract](292) +[HTML](125) +[PDF](480.07KB)
A general multipurpose interpolation procedure: the magic points
Yvon Maday, Ngoc Cuong Nguyen, Anthony T. Patera and S. H. Pau
2009, 8(1) : 383-404 doi: 10.3934/cpaa.2009.8.383 +[Abstract](3138) +[PDF](826.7KB) Cited By(58)
A Brezis-Nirenberg result for non-local critical equations in low dimension
Raffaella Servadei and Enrico Valdinoci
2013, 12(6) : 2445-2464 doi: 10.3934/cpaa.2013.12.2445 +[Abstract](2795) +[PDF](509.5KB) Cited By(57)
A Liouville type Theorem for an integral system
Dezhong Chen and Li Ma
2006, 5(4) : 855-859 doi: 10.3934/cpaa.2006.5.855 +[Abstract](2300) +[PDF](102.3KB) Cited By(57)
Convergence of generalized proximal point algorithms
Giuseppe Marino and Hong-Kun Xu
2004, 3(4) : 791-808 doi: 10.3934/cpaa.2004.3.791 +[Abstract](2306) +[PDF](181.7KB) Cited By(56)
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions
Gianni Gilardi, A. Miranville and Giulio Schimperna
2009, 8(3) : 881-912 doi: 10.3934/cpaa.2009.8.881 +[Abstract](2139) +[PDF](395.6KB) Cited By(46)
The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system$^*$
Lihui Guo, Wancheng Sheng and Tong Zhang
2010, 9(2) : 431-458 doi: 10.3934/cpaa.2010.9.431 +[Abstract](2816) +[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](2173) +[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](2057) +[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](2328) +[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](2127) +[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](3612) +[HTML](399) +[PDF](462.14KB) PDF Downloads(217)
The Nehari manifold for a fractional Laplacian equation involving critical nonlinearities
Qingfang Wang
2018, 17(6) : 2261-2281 doi: 10.3934/cpaa.2018108 +[Abstract](3264) +[HTML](157) +[PDF](409.64KB) PDF Downloads(161)
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](476) +[HTML](154) +[PDF](460.49KB) PDF Downloads(154)
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](2278) +[HTML](210) +[PDF](382.99KB) PDF Downloads(149)
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](2576) +[HTML](153) +[PDF](332.85KB) 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](3005) +[HTML](149) +[PDF](391.77KB) PDF Downloads(141)
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](3351) +[HTML](364) +[PDF](480.5KB) PDF Downloads(141)
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](2974) +[HTML](235) +[PDF](490.86KB) PDF Downloads(137)
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](2049) +[PDF](486.1KB) PDF Downloads(135)
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](2361) +[HTML](193) +[PDF](411.33KB) PDF Downloads(135)

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