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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. CPAA is a bimonthly publication, published in January, March, May, July, September and November. It is edited by a group of energetic leaders to guarantee the journal's highest standard and closest link to the scientific communities.
CPAA is issued jointly by the American Institute of Mathematical Sciences and Shanghai Jiao Tong University. All rights reserved.
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TOP 10 Most Read Articles in CPAA, March 2017
1 
Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion
Volume 9, Number 6, Pages: 1617  1637, 2010
Andrea L. Bertozzi
and Dejan Slepcev
Abstract
Full Text
Related Articles
We present an energymethodsbased proof of the existence and uniqueness of solutions of
a nonlocal aggregation equation with degenerate diffusion. The equation we study
is relevant to models of biological aggregation.

2 
Uniqueness results for noncoercive nonlinear elliptic equations with two lower order terms
Volume 7, Number 1, Pages: 163  192, 2007
Olivier Guibé
and Anna Mercaldo
Abstract
Full Text
Related Articles
In the present paper we prove uniqueness results for weak
solutions to a class of problems whose prototype is
$d i v((1+\nabla u^2)^{(p2)/2} \nabla u)d i v(c(x) (1+u^2)^{(\tau+1)/2}) $
$+b(x) (1+\nabla u^2)^{(\sigma+1)/2}=f \ i n \ \mathcal D'(\Omega)\qquad\qquad\qquad\qquad\qquad\qquad\qquad$
$u\in W^{1,p}_0(\Omega)\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$
where $\Omega$ is a bounded open subset of $\mathbb R^N$ $(N\ge 2)$,
$p$ is a real number $\frac{2N}{N+1}< p <+\infty$, the coefficients
$c(x)$ and $b(x)$ belong to suitable Lebesgue spaces,
$f$ is an element of the dual space $W^{1,p'}(\Omega)$ and $\tau$ and $\sigma$
are positive constants which belong to suitable intervals specified
in Theorem 2.1, Theorem 2.2 and Theorem 2.3.

3 
Hodge decomposition for symmetric matrix fields and the elasticity complex in Lipschitz domains
Volume 8, Number 1, Pages: 295  309, 2008
Giuseppe Geymonat
and Françoise Krasucki
Abstract
Full Text
Related Articles
In 1999 M. Eastwood has used the general construction known as the BernsteinGelfandGelfand (BGG) resolution to prove, at least in smooth situation, the equivalence of the linear elasticity complex and of the de Rham complex in $\mathbf{R}^{3}$. The main objective of this paper is to study the linear elasticity complex for general Lipschitz domains in $\mathbf{R}^{3}$ and deduce a complete Hodge orthogonal decomposition for symmetric matrix fields in $L^{2}$, counterpart of the Hodge decomposition for vector fields. As a byproduct one obtains that the finite dimensional terms of this Hodge decomposition can be interpreted in homological terms as the corresponding terms for the de Rham complex if one takes the homology with value in $RIG\cong \mathbf{R}^{6}$ as in the (BGG) resolution.

4 
A Liouville type Theorem for an integral system
Volume 5, Number 4, Pages: 855  859, 2006
Dezhong Chen
and Li Ma
Abstract
Full Text
Related Articles
In this paper, we study a conjecture of J.Serrin and
give a partial generalized result of the work
of de Figueiredo and Felmer about Liouville type Theorem
for nonnegative solutions for an
elliptic system. We use a new type of moving plane method
introduced by ChenLiOu. Our new ingredient is the use of SteinWeiss
inequality.

5 
Three nontrivial solutions for periodic problems with the $p$Laplacian and a $p$superlinear nonlinearity
Volume 8, Number 4, Pages: 1421  1437, 2009
Leszek Gasiński
and Nikolaos S. Papageorgiou
Abstract
Full Text
Related Articles
We consider a nonlinear periodic problem driven by the scalar
$p$Laplacian and a nonlinearity that exhibits a $p$superlinear growth
near $\pm\infty$, but need not satisfy the AmbrosettiRabinowitz
condition.
Using minimax methods, truncations techniques and Morse theory,
we show that the problem has at least three nontrivial solutions,
two of which are of fixed sign.

6 
Traveling waves and their stability in a coupled reaction diffusion system
Volume 10, Number 1, Pages: 141  160, 2010
Xiaojie Hou
and Wei Feng
Abstract
References
Full Text
Related Articles
We study the traveling wave solutions to a reaction diffusion system
modeling the public goods game with altruistic behaviors. The
existence of the waves is derived through monotone iteration of a
pair of classical upper and lower solutions. The waves are shown to
be unique and strictly monotonic. A similar KPP wave like asymptotic
behaviors are obtained by comparison principle and exponential
dichotomy. The stability of the traveling waves with noncritical
speed is investigated by spectral analysis in the weighted Banach
spaces.

7 
Comparison of numerical methods for fractional differential equations
Volume 5, Number 2, Pages: 289  307, 2006
Joseph A. Connolly
and Neville J. Ford
Abstract
Full Text
Related Articles
In this paper we present a comparison of numerical methods for the solution of single term fractional differential equations. We review five available methods and use a graphical technique to compare their relative merits. We conclude by giving recommendations on the choice of efficient methods for any given single term fractional differential equation.

8 
Asymptotic profiles of eigenfunctions for some 1dimensional linearized eigenvalue problems
Volume 9, Number 2, Pages: 539  561, 2009
Tohru Wakasa
and Shoji Yotsutani
Abstract
Full Text
Related Articles
We are interested in the asymptotic profiles of
all eigenfunctions for 1dimensional
linearized eigenvalue problems
to nonlinear boundary value problems
with a diffusion coefficient $\varepsilon$.
For instance, it seems that
they have simple and beautiful properties
for sufficiently small $\varepsilon$
in the balanced bistable nonlinearity case.
As the first step to give rigorous proofs
for the above case,
we study the case $f(u)=\sin u$ precisely.
We show that two special eigenfunctions completely
control the asymptotic profiles of other eigenfunctions.

9 
On the existence of nodal solutions for singular onedimensional $\varphi$Laplacian problem with asymptotic condition
Volume 7, Number 4, Pages: 905  923, 2008
Inbo Sim
Abstract
Full Text
Related Articles
We obtain the existence results of nodal solutions for singular
onedimensional $\varphi$Laplacian problem with asymptotic
condition:
$\varphi (u'(t))' + \lambda h(t) f (u(t)) = 0,\ \ $ a.e. $\ t \in (0,1), \qquad\qquad\qquad\qquad\qquad $ $(\Phi_\lambda)$
$u(0) = 0=u(1),$
where $\varphi : \mathbb R \to \mathbb R$ is an odd increasing
homeomorphism, $\lambda$ a positive parameter and $h \in L^1(0,1)$ a
nonnegative measurable function on $(0,1)$ which may be singular at
$t = 0$ and/or $t = 1,$ and $f \in C(\mathbb R, \mathbb R)$ and is
odd.

10 
Positive periodic solutions to a nonlinear fourthorder differential equation
Volume 7, Number 5, Pages: 1225  1235, 2008
Chunhua Jin,
Jingxue Yin
and Zejia Wang
Abstract
Full Text
Related Articles
This paper is concerned with the existence of positive periodic solutions to
a nonlinear fourthorder differential equation. By virtue of the first
positive eigenvalue of the linear equation corresponding to the nonlinear
fourth order equation, we establish the existence result by using the fixed
point index theory in a cone.

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