Communications on Pure and Applied Analysis: latest papers http://www.aimsciences.org/test_aims/journals/rss.jsp?journalID=3 Latest articles for selected journal http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8572 Almost global existence for exterior Neumann problems of semilinear wave equations in $2$D http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8572 Soichiro Katayama, Hideo Kubo and Sandra Lucente Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8560 Nontrivial periodic solutions for asymptotically linear hamiltonian systems at resonance http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8560 Shiwang Ma Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8590 Multiple solutions for singular N-Laplace equations with a sign changing nonlinearity http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8590 J. Tyagi Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8561 Asymptotic behavior of the ground state Solutions for Hénon equation with Robin boundary condition http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8561 0, x \in \Omega,\\ \frac{\partial u}{\partial \nu }+\beta u=0, x\in \partial \Omega, \end{eqnarray} where $\Omega$ is the unit ball in $R^N$ centered at the origin with $N\geq 3$, $\alpha>0, \beta>\frac{N-2}{2}, p\geq 2$ and $\nu $ is the unit outward vector normal to $\partial \Omega$. We investigate the asymptotic behavior of the ground state solutions $u_p$ of (1) as $p\to \frac{2N}{N-2}$. We show that the ground state solutions $u_p$ has a unique maximum point $x_p\in \bar\Omega$. In addition, the ground state solutions is non-radial provided that $p\to \frac{2N}{N-2}$. ]]> Haiyang He Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8562 Oblique derivative problems for elliptic and parabolic equations http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8562 Gary Lieberman Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8563 A Brezis-Nirenberg result for non-local critical equations in low dimension http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8563 2s$, with Lipschitz boundary. In the recent papers [14, 18, 19] we investigated the existence of non-trivial solutions for this problem when $\Omega$ is an open bounded subset of $R^n$ with $n\geq 4s$ and, in this framework, we prove some existence results. Aim of this paper is to complete the investigation carried on in [14, 18, 19], by considering the case when $2s < n < 4s$. In this context, we prove an existence theorem for our problem, which may be seen as a Brezis-Nirenberg type result in low dimension. In particular when $s=1$ (and consequently $n=3$) our result is the classical result obtained by Brezis and Nirenberg in the famous paper [4]. In this sense the present work may be considered as the extension of some classical results for the Laplacian to the case of non-local fractional operators. ]]> Raffaella Servadei and Enrico Valdinoci Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8564 Systems of singular integral equations and applications to existence of reversed flow solutions of Falkner-Skan equations http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8564 G. C. Yang and K. Q. Lan Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8591 Super polyharmonic property of solutions for PDE systems and its applications http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8591 0, \ j=1, 2, \cdots, k-1; \ i =1, 2, \cdots, m. \end{eqnarray}
To prove this important super polyharmonic property, we introduced a few new ideas and derived some new estimates.

As an interesting application, we establish the equivalence between the integral system \begin{eqnarray} u_i(x) = \int_{R^n} \frac{1}{|x-y|^{n-\alpha}} f_i(u_1(y), \cdots, u_m(y)) d y, \ x \in R^n \ \ \ \ \ (2) \end{eqnarray} and PDE system (1) when $\alpha = 2k < n.$

In the last few years, a series of results on qualitative properties for solutions of integral systems (2) have been obtained, since the introduction of a powerful tool--the method of moving planes in integral forms. Now due to the equivalence established here, all these properties can be applied to the corresponding PDE systems.

We say that systems (1) and (2) are equivalent, if whenever $u$ is a positive solution of (2), then $u$ is also a solution of \begin{eqnarray} (- \Delta)^k u_i = c f_i(u_1, \cdots, u_m), \ x \in R^n, \ i= 1,2, \cdots, m \end{eqnarray} with some constant $c$; and vice versa. ]]> Wenxiong Chen and Congming Li Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8565 Local uniqueness of steady spherical transonic shock-fronts for the three--dimensional full Euler equations http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8565 Gui-Qiang G. Chen and Hairong Yuan Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8566 Dynamics of vacuum states for one-dimensional full compressible Navier-Stokes equations http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8566 Ben Duan and Zhen Luo Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8567 Weighted Sobolev-Hardy spaces and sign-changing solutions of degenerate elliptic equation http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8567 \frac{\alpha}{2}q+\frac{q}{2^*}-1$. By the compactness result and critical-point theory about sign-changing solutions, we obtain infinitely many sign-changing solutions to a degenerate Dirichlet elliptic equation $-\hbox{div}(d^\alpha \nabla u)- \frac{(1-\alpha )^2}{4} d^{\alpha-2} u=f(x,u)$ provided that $f(x,u)$ satisfies suitable conditions. ]]> Jun Yang and Yaotian Shen Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8568 Four positive solutions of a quasilinear elliptic equation in $ R^N$ http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8568 p$ and $1 < r < p$ $< q < p^* ( = \frac{pN}{N-p})$. A Nehari manifold is defined by a $C^1-$functional $I$ and is decomposed into two parts. Our work is to find four positive solutions of Eq. (1) when parameter $\lambda$ is sufficiently small. ]]> Fang-Fang Liao and Chun-Lei Tang Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8569 Nonexistence of positive solutions for a system of integral equations on $R^n_+$ and applications http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8569 1$. Nonexistence of positive solution is proved by using the method of moving planes in integral forms. We also obtain the equivalence between the system of integral equations and corresponding partial differential equations. ]]> Dongyan Li and Yongzhong Wang Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8570 A stability result for the Stokes-Boussinesq equations in infinite 3d channels http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8570 Marta Lewicka and Mohammadreza Raoofi Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8571 Blowup threshold and collapse mass separation for a drift-diffusion system in space-dimension two http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8571 Elio E. Espejo, Masaki Kurokiba and Takashi Suzuki Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8573 Decay rates for Kirchhoff-Timoshenko transmission problems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8573 Tamara Fastovska Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8574 Long time dynamics for forced and weakly damped KdV on the torus http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8574 M. Burak Erdoğan and Nikolaos Tzirakis Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8575 Regularity, symmetry and uniqueness of positive solutions to a nonlinear elliptic system http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8575 1$ and $p+q<\frac{n+\alpha-\beta}{n-\alpha+\beta}$. We show that positive solutions of the system are radially symmetric and belong to $L^\infty(R^n)$, which possibly implies that the solutions are locally Hölder continuous. Moreover, if $ \alpha=2, \beta =0,p\le q$, we show that positive solution pair $(u,v)$ of the system is unique and $u=v = U$, where $U$ is the unique positive solution of the problem \begin{eqnarray} -\Delta u + u = u^{p+q}\quad {\rm in}\quad \mathbb{R}^n. \end{eqnarray} ]]> Shiren Zhu, Xiaoli Chen and Jianfu Yang Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8589 Elliptic equations involving linear and superlinear terms and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8589 Mateus Balbino Guimarães and Rodrigo da Silva Rodrigues Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8576 Logarithmically improved criteria for Euler and Navier-Stokes equations http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8576 Yi Zhou and Zhen Lei Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8578 Positive solutions of integral systems involving Bessel potentials http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8578 Yutian Lei Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8579 Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems of diagonal form with large BV data http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8579 Zhi-Qiang Shao Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8580 On general fractional abstract Cauchy problem http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8580 Zhan-Dong Mei, Ji-Gen Peng and Yang Zhang Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8581 Existence and multiplicity of solutions for Kirchhoff type problem with critical exponent http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8581 Qi-Lin Xie, Xing-Ping Wu and Chun-Lei Tang Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8582 Convergence rates for elliptic reiterated homogenization problems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8582 Jie Zhao Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8583 Analytic integrability for some degenerate planar systems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8583 Antonio Algaba, Cristóbal García and Jaume Giné Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8584 Well-posedness and long time behavior of an Allen-Cahn type equation http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8584 Haydi Israel Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8585 Remarks on the approximation of the Navier-Stokes equations via the implicit Euler scheme http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8585 Michele Coti Zelati Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8586 Eigenvalues, bifurcation and one-sign solutions for the periodic $p$-Laplacian http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8586 Guowei Dai, Ruyun Ma and Haiyan Wang Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8587 Regularity criteria of smooth solution to the incompressible viscoelastic flow http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8587 Hua Qiu Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8588 Solutions of nonlinear nonhomogeneous Neumann and Dirichlet problems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8588 Shouchuan Hu and Perikles G. Papadopoulos Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8553 A double saddle-node bifurcation theorem http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8553 Ping Liu, Junping Shi and Yuwen Wang Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8554 Blow-up for a non-local diffusion equation with exponential reaction term and Neumann boundary condition http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8554 Shouming Zhou, Chunlai Mu, Yongsheng Mi and Fuchen Zhang Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8555 Free vibrations in space of the single mode for the Kirchhoff string http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8555 Clelia Marchionna Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8556 Non-isothermal cyclic fatigue in an oscillating elastoplastic beam http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8556 Michela Eleuteri, Jana Kopfová and Pavel Krejčí Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8557 Bifurcations and periodic orbits in variable population interactions http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8557 Jorge Rebaza Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8558 On symmetry results for elliptic equations with convex nonlinearities http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8558 Kanishka Perera and Marco Squassina Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8559 Global dynamics and diffusion limit of a one-dimensional repulsive chemotaxis model http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8559 Zhi-An Wang and Kun Zhao Fri, 1 Nov 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8577 Pullback exponential attractors for evolution processes in Banach spaces: Theoretical results http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8577 Alexandre Nolasco de Carvalho and Stefanie Sonner Fri, 1 Nov 2013 08:00:00 GMT