Communications on Pure and Applied Analysis: latest papers Latest articles for selected journal Local well-posedness for 2-D Schrödinger equation on irrational tori and bounds on Sobolev norms \frac{131}{416}$. We also obtain improved growth bounds for higher order Sobolev norms. ]]> Seckin Demirbas Fri, 1 Sep 2017 20:00:00 GMT Existence of multiple positive weak solutions and estimates for extremal values for a class of concave-convex elliptic problems with an inverse-square potential 0$ 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 On uniform estimate of complex elliptic equations on closed Hermitian manifolds Wei Sun Fri, 1 Sep 2017 20:00:00 GMT Exponential boundary stabilization for nonlinear wave equations with localized damping and nonlinear boundary condition Takeshi Taniguchi Fri, 1 Sep 2017 20:00:00 GMT Multiple positive solutions for Schrödinger-Poisson system in $\mathbb{R}^{3}$ involving concave-convex nonlinearities with critical exponent 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 Positive solutions for quasilinear Schrödinger equations in $\mathbb{R}^N$ 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 Gevrey regularity and existence of Navier-Stokes-Nernst-Planck-Poisson system in critical Besov spaces 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 Existence and concentration for Kirchhoff type equations around topologically critical points of the potential Yu Chen, Yanheng Ding and Suhong Li Fri, 1 Sep 2017 20:00:00 GMT Semilinear damped wave equation in locally uniform spaces Martin Michálek, Dalibor Pražák and Jakub Slavík Fri, 1 Sep 2017 20:00:00 GMT A new second critical exponent and life span for a quasilinear degenerate parabolic equation with weighted nonlocal sources 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 A direct method of moving planes for a fully nonlinear nonlocal system 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 Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schrödinger operators 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 Low Mach number limit of the full compressible Hall-MHD system Jishan Fan, Fucai Li and Gen Nakamura Fri, 1 Sep 2017 20:00:00 GMT Semilinear nonlocal elliptic equations with critical and supercritical exponents 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 On some local-nonlocal elliptic equation involving nonlinear terms with exponential growth Sami Aouaoui Fri, 1 Sep 2017 20:00:00 GMT Segregated vector solutions for nonlinear Schrödinger systems with electromagnetic potentials Jing Yang Fri, 1 Sep 2017 20:00:00 GMT Layered solutions to the vector Allen-Cahn equation in $R^2$. Minimizers and heteroclinic connections $\qquad$ 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 Optimality conditions of the first eigenvalue of a fourth order Steklov problem Monika Laskawy Fri, 1 Sep 2017 20:00:00 GMT Global well-posedness of the two-dimensional horizontally filtered simplified Bardina turbulence model on a strip-like region Luca Bisconti and Davide Catania Fri, 1 Sep 2017 20:00:00 GMT Global dynamics of a microorganism flocculation model with time delay Songbai Guo and Wanbiao Ma Fri, 1 Sep 2017 20:00:00 GMT Dynamics of some stochastic chemostat models with multiplicative noise Tomás Caraballo, María J. Garrido–Atienza and J. López-de-la-Cruz Fri, 1 Sep 2017 20:00:00 GMT Structure-preserving finite difference schemes for the Cahn--Hilliard equation with dynamic boundary conditions in the one-dimensional case Takeshi Fukao, Shuji Yoshikawa and Saori Wada Fri, 1 Sep 2017 20:00:00 GMT Corrigendum to "On small data scattering of Hartree equations with short-range interaction" [Comm. Pure. Appl. Anal., 15 (2016), 1809--1823] Yonggeun Cho, Gyeongha Hwang and Tohru Ozawa Fri, 1 Sep 2017 20:00:00 GMT