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Communications on Pure & Applied Analysis (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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Response solutions to harmonic oscillators beyond multi–dimensional Brjuno frequency
Hongyu Cheng and Shimin Wang
2021, 20(2) : 467-494 doi: 10.3934/cpaa.2020222 +[Abstract](356) +[HTML](75) +[PDF](450.54KB)
On the Cahn-Hilliard equation with mass source for biological applications
Hussein Fakih, Ragheb Mghames and Noura Nasreddine
2021, 20(2) : 495-510 doi: 10.3934/cpaa.2020277 +[Abstract](292) +[HTML](72) +[PDF](1413.88KB)
Topological Equivalence of nonautonomous difference equations with a family of dichotomies on the half line
Álvaro Castañeda, Pablo González and Gonzalo Robledo
2021, 20(2) : 511-532 doi: 10.3934/cpaa.2020278 +[Abstract](300) +[HTML](75) +[PDF](433.38KB)
Homogenization and singular perturbation in porous media
Eduard Marušić-Paloka and Igor Pažanin
2021, 20(2) : 533-545 doi: 10.3934/cpaa.2020279 +[Abstract](310) +[HTML](100) +[PDF](340.46KB)
A unique continuation property for a class of parabolic differential inequalities in a bounded domain
Guojie Zheng, Dihong Xu and Taige Wang
2021, 20(2) : 547-558 doi: 10.3934/cpaa.2020280 +[Abstract](339) +[HTML](73) +[PDF](331.74KB)
Classification and evolution of bifurcation curves for a porous-medium combustion problem with large activation energy
Kuo-Chih Hung and Shin-Hwa Wang
2021, 20(2) : 559-582 doi: 10.3934/cpaa.2020281 +[Abstract](314) +[HTML](80) +[PDF](424.61KB)
Semilinear Caputo time-fractional pseudo-parabolic equations
Nguyen Huy Tuan, Vo Van Au and Runzhang Xu
2021, 20(2) : 583-621 doi: 10.3934/cpaa.2020282 +[Abstract](399) +[HTML](176) +[PDF](508.12KB)
Dimension estimate of attractors for complex networks of reaction-diffusion systems applied to an ecological model
Guillaume Cantin and M. A. Aziz-Alaoui
2021, 20(2) : 623-650 doi: 10.3934/cpaa.2020283 +[Abstract](295) +[HTML](68) +[PDF](1813.66KB)
Random data theory for the cubic fourth-order nonlinear Schrödinger equation
Van Duong Dinh
2021, 20(2) : 651-680 doi: 10.3934/cpaa.2020284 +[Abstract](361) +[HTML](58) +[PDF](465.57KB)
Dual spaces of mixed-norm martingale Hardy spaces
Ferenc Weisz
2021, 20(2) : 681-695 doi: 10.3934/cpaa.2020285 +[Abstract](243) +[HTML](72) +[PDF](364.07KB)
Elliptic problems with rough boundary data in generalized Sobolev spaces
Anna Anop, Robert Denk and Aleksandr Murach
2021, 20(2) : 697-735 doi: 10.3934/cpaa.2020286 +[Abstract](288) +[HTML](74) +[PDF](515.58KB)
Almost global existence for the Klein-Gordon equation with the Kirchhoff-type nonlinearity
Zheng Han and Daoyuan Fang
2021, 20(2) : 737-754 doi: 10.3934/cpaa.2020287 +[Abstract](259) +[HTML](63) +[PDF](381.34KB)
Single species population dynamics in seasonal environment with short reproduction period
Attila Dénes and Gergely Röst
2021, 20(2) : 755-762 doi: 10.3934/cpaa.2020288 +[Abstract](287) +[HTML](83) +[PDF](587.42KB)
Further regularity and uniqueness results for a non-isothermal Cahn-Hilliard equation
Erica Ipocoana and Andrea Zafferi
2021, 20(2) : 763-782 doi: 10.3934/cpaa.2020289 +[Abstract](244) +[HTML](60) +[PDF](363.11KB)
The anisotropic fractional isoperimetric problem with respect to unconditional unit balls
Andreas Kreuml
2021, 20(2) : 783-799 doi: 10.3934/cpaa.2020290 +[Abstract](195) +[HTML](54) +[PDF](362.47KB)
The boundedness of multi-linear and multi-parameter pseudo-differential operators
Liang Huang and Jiao Chen
2021, 20(2) : 801-815 doi: 10.3934/cpaa.2020291 +[Abstract](234) +[HTML](63) +[PDF](347.22KB)
Ground state and nodal solutions for fractional Schrödinger-Maxwell-Kirchhoff systems with pure critical growth nonlinearity
Chungen Liu and Huabo Zhang
2021, 20(2) : 817-834 doi: 10.3934/cpaa.2020292 +[Abstract](237) +[HTML](60) +[PDF](394.47KB)
Sub-solutions and a point-wise Hopf's lemma for fractional $ p $-Laplacian
Zaizheng Li and Qidi Zhang
2021, 20(2) : 835-865 doi: 10.3934/cpaa.2020293 +[Abstract](266) +[HTML](60) +[PDF](490.8KB)
Multiple positive solutions for coupled Schrödinger equations with perturbations
Haoyu Li and Zhi-Qiang Wang
2021, 20(2) : 867-884 doi: 10.3934/cpaa.2020294 +[Abstract](254) +[HTML](61) +[PDF](463.51KB)
On the quotient quantum graph with respect to the regular representation
Gökhan Mutlu
2021, 20(2) : 885-902 doi: 10.3934/cpaa.2020295 +[Abstract](209) +[HTML](53) +[PDF](331.92KB)
Inequalities of Hermite-Hadamard type for higher order convex functions, revisited
Tomasz Szostok
2021, 20(2) : 903-914 doi: 10.3934/cpaa.2020296 +[Abstract](237) +[HTML](55) +[PDF](455.31KB)
The degenerate Monge-Ampère equations with the Neumann condition
Juhua Shi and Feida Jiang
2021, 20(2) : 915-931 doi: 10.3934/cpaa.2020297 +[Abstract](223) +[HTML](47) +[PDF](372.98KB)
Ground states for a class of quasilinear Schrödinger equations with vanishing potentials
Zhouxin Li and Yimin Zhang
2021, 20(2) : 933-954 doi: 10.3934/cpaa.2020298 +[Abstract](233) +[HTML](57) +[PDF](466.6KB)
Blow-up results for effectively damped wave models with nonlinear memory
Tayeb Hadj Kaddour and Michael Reissig
2020doi: 10.3934/cpaa.2020239 +[Abstract](563) +[HTML](217) +[PDF](338.09KB)
Remark on 3-D Navier-Stokes system with strong dissipation in one direction
Yanlin Liu and Ping Zhang
2020doi: 10.3934/cpaa.2020244 +[Abstract](437) +[HTML](194) +[PDF](383.55KB)
The two-component Novikov-type systems with peaked solutions and $ H^1 $-conservation law
Min Zhao and Changzheng Qu
2020doi: 10.3934/cpaa.2020245 +[Abstract](487) +[HTML](210) +[PDF](367.37KB)
Multiple solutions for nonlinear cone degenerate elliptic equations
Hua Chen and Yawei Wei
2020doi: 10.3934/cpaa.2020272 +[Abstract](393) +[HTML](136) +[PDF](319.1KB)
Global existence and uniform estimates of solutions to reaction diffusion systems with mass transport type boundary conditions
Vandana Sharma
2021doi: 10.3934/cpaa.2021001 +[Abstract](230) +[HTML](82) +[PDF](319.92KB)
Discrete diffusion semigroups associated with Jacobi-Dunkl and exceptional Jacobi polynomials
Ágota P. Horváth
2021doi: 10.3934/cpaa.2021002 +[Abstract](157) +[HTML](96) +[PDF](386.52KB)
Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping
Qiwei Wu and Liping Luan
2021doi: 10.3934/cpaa.2021003 +[Abstract](215) +[HTML](81) +[PDF](359.76KB)
An overdetermined problem associated to the Finsler Laplacian
Giulio Ciraolo and Antonio Greco
2021doi: 10.3934/cpaa.2021004 +[Abstract](216) +[HTML](96) +[PDF](332.29KB)
Polynomial growth of high sobolev norms of solutions to the Zakharov-Kuznetsov equation
Raphaël Côte and Frédéric Valet
2021doi: 10.3934/cpaa.2021005 +[Abstract](122) +[HTML](62) +[PDF](405.28KB)
Well-posedness and attractor for a strongly damped wave equation with supercritical nonlinearity on $ \mathbb{R}^{N} $
Pengyan Ding and Zhijian Yang
2021doi: 10.3934/cpaa.2021006 +[Abstract](137) +[HTML](69) +[PDF](388.66KB)
Rational limit cycles of abel equations
Jaume Llibre and Claudia Valls
2021doi: 10.3934/cpaa.2021007 +[Abstract](120) +[HTML](66) +[PDF](284.28KB)
Scale pressure for amenable group actions
Dandan Cheng, Qian Hao and Zhiming Li
2021doi: 10.3934/cpaa.2021008 +[Abstract](135) +[HTML](58) +[PDF](304.83KB)
Boundary-Domain Integral Equations equivalent to an exterior mixed bvp for the variable-viscosity compressible stokes pdes
Sergey E. Mikhailov and Carlos F. Portillo
2021doi: 10.3934/cpaa.2021009 +[Abstract](124) +[HTML](62) +[PDF](485.75KB)
Approximation of a stochastic two-phase flow model by a splitting-up method
G. Deugoué, B. Jidjou Moghomye and T. Tachim Medjo
2021doi: 10.3934/cpaa.2021010 +[Abstract](64) +[HTML](38) +[PDF](529.05KB)
The BSE concepts for vector-valued Lipschitz algebras
Fatemeh Abtahi, Zeinab Kamali and Maryam Toutounchi
2021doi: 10.3934/cpaa.2021011 +[Abstract](83) +[HTML](39) +[PDF](321.97KB)
The interior gradient estimate of prescribed Hessian quotient curvature equation in the hyperbolic space
Xinqun Mei and Jundong Zhou
2021doi: 10.3934/cpaa.2021012 +[Abstract](68) +[HTML](37) +[PDF](337.45KB)
Kuramoto order parameters and phase concentration for the Kuramoto-Sakaguchi equation with frustration
Seung-Yeal Ha, Javier Morales and Yinglong Zhang
2021doi: 10.3934/cpaa.2021013 +[Abstract](70) +[HTML](43) +[PDF](496.32KB)
Global solutions of a two-dimensional Riemann problem for the pressure gradient system
Gui-Qiang G. Chen, Qin Wang and Shengguo Zhu
2021doi: 10.3934/cpaa.2021014 +[Abstract](74) +[HTML](75) +[PDF](643.44KB)
On a supersonic-sonic patch arising from the frankl problem in transonic flows
Yanbo Hu and Jiequan Li
2021doi: 10.3934/cpaa.2021015 +[Abstract](72) +[HTML](38) +[PDF](463.0KB)
Cylindrical estimates for mean curvature flow in hyperbolic spaces
Zhengchao Ji
2021doi: 10.3934/cpaa.2021016 +[Abstract](20) +[HTML](16) +[PDF](322.29KB)
Existence of solution and asymptotic behavior for a class of parabolic equations
Anderson L. A. de Araujo and Marcelo Montenegro
2021doi: 10.3934/cpaa.2021017 +[Abstract](17) +[HTML](13) +[PDF](375.98KB)
Global well-posedness of the $ n $-dimensional hyper-dissipative Boussinesq system without thermal diffusivity
Xuemin Deng, Yuelong Xiao and Aibin Zang
2021doi: 10.3934/cpaa.2021018 +[Abstract](16) +[HTML](12) +[PDF](398.44KB)
Classification of positive solutions for fully nonlinear elliptic equations in unbounded cylinders
Lidan Wang, Lihe Wang and Chunqin Zhou
2021doi: 10.3934/cpaa.2021019 +[Abstract](18) +[HTML](12) +[PDF](424.67KB)
Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation
Jihoon Lee and Nguyen Thanh Nguyen
2021doi: 10.3934/cpaa.2021020 +[Abstract](31) +[HTML](18) +[PDF](497.77KB)
Stability of rarefaction wave for the compressible non-isentropic Navier-Stokes-Maxwell equations
Huancheng Yao, Haiyan Yin and Changjiang Zhu
2021doi: 10.3934/cpaa.2021021 +[Abstract](26) +[HTML](18) +[PDF](464.06KB)
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](2945) +[PDF](225.5KB) Cited By(106)
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](4956) +[PDF](826.7KB) Cited By(103)
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](2718) +[HTML](230) +[PDF](373.99KB) Cited By(95)
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](4535) +[PDF](509.5KB) Cited By(91)
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](4072) +[PDF](181.7KB) Cited By(89)
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](2250) +[PDF](130.3KB) Cited By(75)
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](4157) +[PDF](1276.3KB) Cited By(70)
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](3423) +[PDF](395.6KB) 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](3564) +[PDF](102.3KB) Cited By(68)
Quasilinear Schrödinger equations involving concave and convex nonlinearities
João Marcos do Ó and Uberlandio Severo
2009, 8(2) : 621-644 doi: 10.3934/cpaa.2009.8.621 +[Abstract](2808) +[PDF](274.6KB) Cited By(66)
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](3643) +[PDF](486.1KB) PDF Downloads(431)
Bifurcation and stability of a two-species diffusive Lotka-Volterra model
Li Ma and Shangjiang Guo
2020, 19(3) : 1205-1232 doi: 10.3934/cpaa.2020056 +[Abstract](1864) +[HTML](80) +[PDF](419.64KB) PDF Downloads(400)
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](4458) +[HTML](221) +[PDF](328.43KB) PDF Downloads(358)
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](4083) +[HTML](360) +[PDF](342.33KB) PDF Downloads(355)
Kirchhoff type equations with strong singularities
Yijing Sun and Yuxin Tan
2019, 18(1) : 181-193 doi: 10.3934/cpaa.2019010 +[Abstract](3890) +[HTML](209) +[PDF](342.2KB) PDF Downloads(351)
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
2020, 19(8) : 4213-4225 doi: 10.3934/cpaa.2020189 +[Abstract](644) +[HTML](82) +[PDF](414.25KB) PDF Downloads(328)
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](2033) +[HTML](266) +[PDF](460.49KB) PDF Downloads(325)
Translating solutions of non-parametric mean curvature flows with capillary-type boundary value problems
Jun Wang, Wei Wei and Jinju Xu
2019, 18(6) : 3243-3265 doi: 10.3934/cpaa.2019146 +[Abstract](1743) +[HTML](211) +[PDF](407.02KB) PDF Downloads(325)
Mean value properties and unique continuation
José G. Llorente
2015, 14(1) : 185-199 doi: 10.3934/cpaa.2015.14.185 +[Abstract](2400) +[PDF](427.4KB) PDF Downloads(322)
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](1089) +[HTML](163) +[PDF](356.02KB) PDF Downloads(311)

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