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=14102 Local well-posedness for 2-D Schrödinger equation on irrational tori and bounds on Sobolev norms http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14102 \frac{131}{416}$. We also obtain improved growth bounds for higher order Sobolev norms. ]]> Seckin Demirbas Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14103 Existence of multiple positive weak solutions and estimates for extremal values for a class of concave-convex elliptic problems with an inverse-square potential http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14103 0$ is a parameter, $0 < \lambda < \Lambda =\frac{(N-2)^2}{4}$, $0 < q < 1 < p < 2^\ast-1$, $h(x)>0$ and $W(x)$ is a given function with the set $\{x\in \Omega: W(x)>0\}$ of positive measure. ]]> Yaoping Chen and Jianqing Chen Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14104 On uniform estimate of complex elliptic equations on closed Hermitian manifolds http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14104 Wei Sun Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14105 Exponential boundary stabilization for nonlinear wave equations with localized damping and nonlinear boundary condition http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14105 Takeshi Taniguchi Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14106 Multiple positive solutions for Schrödinger-Poisson system in $\mathbb{R}^{3}$ involving concave-convex nonlinearities with critical exponent http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14106 0$. Under some appropriate conditions on $l$ and $h$, we show that there exists $\lambda^{*}>0$ such that the above problem has at least two positive solutions for each $\lambda\in (0,\lambda^{*})$ by using the Mountain Pass Theorem and Ekeland's Variational Principle. ]]> Miao-Miao Li and Chun-Lei Tang Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14107 Positive solutions for quasilinear Schrödinger equations in $\mathbb{R}^N$ http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14107 0$ as $|x|\to\infty$ and $g\in C(\mathbb{R},\mathbb{R})$. We prove the existence of positive solutions by using the Nehari manifold. ]]> Xiang-Dong Fang Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14108 Gevrey regularity and existence of Navier-Stokes-Nernst-Planck-Poisson system in critical Besov spaces http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14108 J. Funct. Anal., 87 (1989), 359-369], we prove that the solutions are analytic in a Gevrey class of functions. As a consequence of Gevrey estimates, we particularly obtain higher-order derivatives of solutions in Besov and Lebesgue spaces. Finally, we prove that there exists a positive constant $\mathbb{C}$ such that if the initial data $(u_{0}, n_{0}, c_{0})=(u_{0}^{h}, u_{0}^{3}, n_{0}, c_{0})$ satisfies \begin{equation} \|(n_{0}, c_{0},u_{0}^{h}) \|_{\dot{B}^{-2+3/q}_{q, 1}\times \dot{B}^{-2+3/q}_{q, 1} \times \dot{B}^{-1+3/p}_{p, 1}} + \|u_{0}^{h}\|_{\dot{B}^{-1+3/p}_{p, 1}}^{\alpha} \|u_{0}^{3}\|_{\dot{B}^{-1+3/p}_{p, 1}}^{1-\alpha} \leq 1/\mathbb{C} \end{equation} for $p, q, \alpha$ with $1 < p < q \leq 2p < \infty, \frac{1}{p}+\frac{1}{q} > \frac{1}{3}, 1 < q < 6, \frac{1}{p}-\frac{1}{q}\leq \frac{1}{3}$, then global existence of solutions with large initial vertical velocity component is established. ]]> Minghua Yang and Jinyi Sun Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14109 Existence and concentration for Kirchhoff type equations around topologically critical points of the potential http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14109 Yu Chen, Yanheng Ding and Suhong Li Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14110 Semilinear damped wave equation in locally uniform spaces http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14110 Martin Michálek, Dalibor Pražák and Jakub Slavík Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14111 A new second critical exponent and life span for a quasilinear degenerate parabolic equation with weighted nonlocal sources http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14111 2$, $q$, $r\geq1$, $s\geq0$, and $r+s>1$. We classify global and non-global solutions of the equation in the coexistence region by finding a new second critical exponent via the slow decay asymptotic behavior of an initial value at spatial infinity, and the life span of non-global solution is studied. ]]> Lingwei Ma and Zhong Bo Fang Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14112 A direct method of moving planes for a fully nonlinear nonlocal system http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14112 1,$ $k_1(x),k_2(x)\geq0.$
$\qquad$ A narrow region principle and a decay at infinity are established for carrying on the method of moving planes. Then we prove the radial symmetry and monotonicity for positive solutions to the nonlinear system in the whole space. Furthermore non-existence of positive solutions to the system on a half space is derived. ]]>
Pengyan Wang and Pengcheng Niu Fri, 1 Sep 2017 20:00:00 GMT
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14113 Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schrödinger operators http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14113 0$ an $L$-independent constant. The exponential decay condition on $\phi$ can alternatively be formulated as an exponential decay condition of the map $\lambda \mapsto \|\chi_{[\lambda , \infty)} (H_L) \phi \|^2$. The novelty is that at the same time we allow the function $\phi$ to be from an infinite dimensional spectral subspace and keep an explicit control over the constant $C_{s f u c}$ in terms of the parameters. Moreover, we show that a similar result cannot hold under a polynomial decay condition. ]]> Matthias Täufer and Martin Tautenhahn Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14114 Low Mach number limit of the full compressible Hall-MHD system http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14114 Jishan Fan, Fucai Li and Gen Nakamura Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14115 Semilinear nonlocal elliptic equations with critical and supercritical exponents http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14115 0 \quad\text{in}\quad\mathbb{R}^N, \end{aligned} \right. \end{equation} where $s\in(0,1)$ is a fixed parameter, $(-\Delta)^s$ is the fractional Laplacian in $\mathbb{R}^N$, $q > p \geq \frac{N+2s}{N-2s}$ and $N>2s$. For every $s\in(0,1)$, we establish regularity results of solutions of above equation (whenever solution exists) and we show that every solution is a classical solution. Next, we derive certain decay estimate of solutions and the gradient of solutions at infinity for all $s\in (0,1)$. Using those decay estimates, we prove Pohozaev type identity in $R^n$ and we show that the above problem does not have any solution when $p=\frac{N+2s}{N-2s}$. We also discuss radial symmetry and decreasing property of the solution and prove that when $p>\frac{N+2s}{N-2s}$, the above problem admits a solution . Moreover, if we consider the above equation in a bounded domain with Dirichlet boundary condition, we prove that it admits a solution for every $p\geq \frac{N+2s}{N-2s}$ and every solution is a classical solution. ]]> Mousomi Bhakta and Debangana Mukherjee Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14116 On some local-nonlocal elliptic equation involving nonlinear terms with exponential growth http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14116 Sami Aouaoui Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14117 Segregated vector solutions for nonlinear Schrödinger systems with electromagnetic potentials http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14117 Jing Yang Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14118 Layered solutions to the vector Allen-Cahn equation in $R^2$. Minimizers and heteroclinic connections http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14118 $\qquad$ We first consider the problem of characterizing the minimizers $u: R^n \rightarrow R^m$ of the energy $\mathcal{J}_\Omega(u)=\int_\Omega (\frac{|\nabla u|^2}{2}+W(u)){d} x$. Under a nondegeneracy condition on $\bar{u}_j$, $j=1,\ldots,N$ and in two space dimensions, we prove that, provided it remains away from $a_-$ and $a_+$ in corresponding half spaces $S_-$ and $S_+$, a bounded minimizer $u: R^2 \rightarrow R^m$ is necessarily an heteroclinic connection between suitable translates $\bar{u}_-(\cdot-\eta_-)$ and $\bar{u}_+(\cdot-\eta_+)$ of some $\bar{u}_\pm \in \{\bar{u}_1,\ldots,\bar{u}_N \}$.
$\qquad$ Then we focus on the existence problem and assuming $N=2$ and denoting $\bar{u}_-,\bar{u}_+$ the representations of the two orbits connecting $a_-$ to $a_+$ we give a new proof of the existence (first proved in [32]) of a solution $u: R^2\rightarrow R^m$ of \begin{equation} \Delta u=W_u(u), \end{equation} that connects certain translates of $\bar{u}_\pm$. ]]>
Giorgio Fusco Fri, 1 Sep 2017 20:00:00 GMT
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14119 Optimality conditions of the first eigenvalue of a fourth order Steklov problem http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14119 Monika Laskawy Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14120 Global well-posedness of the two-dimensional horizontally filtered simplified Bardina turbulence model on a strip-like region http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14120 Luca Bisconti and Davide Catania Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14121 Global dynamics of a microorganism flocculation model with time delay http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14121 Songbai Guo and Wanbiao Ma Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14122 Dynamics of some stochastic chemostat models with multiplicative noise http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14122 Tomás Caraballo, María J. Garrido–Atienza and J. López-de-la-Cruz Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14123 Structure-preserving finite difference schemes for the Cahn--Hilliard equation with dynamic boundary conditions in the one-dimensional case http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14123 Takeshi Fukao, Shuji Yoshikawa and Saori Wada Fri, 1 Sep 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14124 Corrigendum to "On small data scattering of Hartree equations with short-range interaction" [Comm. Pure. Appl. Anal., 15 (2016), 1809--1823] http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14124 Yonggeun Cho, Gyeongha Hwang and Tohru Ozawa Fri, 1 Sep 2017 20:00:00 GMT