Discrete and Continuous Dynamical Systems - Series A: latest papers http://www.aimsciences.org/test_aims/journals/rss.jsp?journalID=1 Latest articles for selected journal http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13977 Regularity of extremal solutions of semilinear elliptic problems with non-convex nonlinearities on general domains http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13977 \frac{1}{2} $ or $ \frac{1}{2} < \beta_{-} \leq \beta_{+} < \frac{7}{10} $, then $ u^{*} \in L^{\infty}(\Omega) $, for $ n \leq 9 $. Moreover, under the sole condition that $ \beta_{-} > \frac{1}{2} $ we have $ u^{*} \in H^{1}_{0}(\Omega) $ for $ n \geq 1 $. The same is true if for some $ \epsilon > 0 $ we have $$ \frac{tf'(t)}{f(t)} \geq 1+\frac{1}{(\ln t)^{2-\epsilon}} ~~ \text{for large} ~ t, $$ which improves a similar result by Brezis and Vázquez [4]. ]]> Asadollah Aghajani Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13978 Topological stability from Gromov-Hausdorff viewpoint http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13978 $C^0$-Gromov-Hausdorff distance between maps of possibly different metric spaces. The latter is then combined with Walters's topological stability [11] to obtain the notion of topologically GH-stable homeomorphism. We prove that there are topologically stable homeomorphism which are not topologically GH-stable. Also that every topological GH-stable circle homeomorphism is topologically stable. Afterwards, we prove that every expansive homeomorphism with the pseudo-orbit tracing property of a compact metric space is topologically GH-stable. This is related to Walters's stability theorem [11]. Finally, we extend the topological GH-stability to continuous maps and prove the constant maps on compact homogeneous manifolds are topologically GH-stable. ]]> Alexander Arbieto and Carlos Arnoldo Morales Rojas Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13979 Sliding Hopf bifurcation in interval systems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13979 Edward Hooton, Zalman Balanov, Wieslaw Krawcewicz and Dmitrii Rachinskii Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13980 Singular perturbations of Blaschke products and connectivity of Fatou components http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13980 Jordi Canela Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13981 Monotonicity and symmetry of solutions to fractional Laplacian equation http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13981 0, & \qquad x\in{\Omega}, \\ u(x)\equiv0, & \qquad x\notin{\Omega}. \end{array}\right.                      (1) \label{p1} \end{equation}
    In this paper, instead of using the conventional extension method introduced by Caffarelli and Silvestre, we employ a direct method of moving planes for the fractional Laplacian to obtain the monotonicity and symmetry of the positive solutions of a semi-linear equation involving the fractional Laplacian. By using the integral definition of the fractional Laplacian, we first introduce various maximum principles which play an important role in the process of moving planes. Then we establish the monotonicity and symmetry of positive solutions of the semi-linear equations involving the fractional Laplacian. ]]>
Tingzhi Cheng Sat, 1 Jul 2017 08:00:00 GMT
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13982 On a definition of Morse-Smale evolution processes http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13982 Radosław Czaja, Waldyr M. Oliva and Carlos Rocha Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13983 Classical solvability of the multidimensional free boundary problem for the thin film equation with quadratic mobility in the case of partial wetting http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13983 Sergey Degtyarev Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13984 Thermodynamic formalism and $k$-bonacci substitutions http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13984 Jordan Emme Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13985 Metastable energy strata in numerical discretizations of weakly nonlinear wave equations http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13985 Ludwig Gauckler and Daniel Weiss Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13986 Blow-up solutions for two coupled Gross-Pitaevskii equations with attractive interactions http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13986 Yujin Guo, Xiaoyu Zeng and Huan-Song Zhou Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13987 Measure-preservation criteria for a certain class of 1-Lipschitz functions on $Z_p$ in Mahler's expansion http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13987 Sangtae Jeong and Chunlan Li Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13988 Conjugacies of model sets http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13988 Johannes Kellendonk and Lorenzo Sadun Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13989 The energy-critical NLS with inverse-square potential http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13989 -\frac14 +\frac1{25}$. We also carry out the variational analysis needed to treat the focusing case. ]]> Rowan Killip, Changxing Miao, Monica Visan, Junyong Zhang and Jiqiang Zheng Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13990 Uniformly expanding Markov maps of the real line: Exactness and infinite mixing http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13990 Marco Lenci Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13991 Existence of SRB measures for a class of partially hyperbolic attractors in banach spaces http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13991 Zeng Lian, Peidong Liu and Kening Lu Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13992 Strong solutions to Cauchy problem of 2D compressible nematic liquid crystal flows http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13992 2$) of the velocity $u$ cannot be controlled in terms only of $\rho^{\frac{1}{2}}u$ and $\nabla u$ here. In the present paper, under the framework of weighted approximation estimates introduced in [J. Li, Z. Liang, On classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations with vacuum, J. Math. Pures Appl. (2014) 640--671] for Navier-Stokes equations, we obtain the local existence of strong solutions to the 2D compressible nematic liquid crystal flows. ]]> Yang Liu, Sining Zheng, Huapeng Li and Shengquan Liu Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13993 Dynamical properties of nonautonomous functional differential equations with state-dependent delay http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13993 Ismael Maroto, Carmen Núñez and Rafael Obaya Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13994 Least energy solutions for nonlinear Schrödinger equation involving the fractional Laplacian and critical growth http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13994 Miaomiao Niu and Zhongwei Tang Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13995 Variational properties and linear stabilities of spatial isosceles orbits in the equal-mass three-body problem http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13995 Tiancheng Ouyang and Duokui Yan Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13996 Typical points and families of expanding interval mappings http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13996 Tomas Persson Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13997 A diffusion problem of Kirchhoff type involving the nonlocal fractional $p$--Laplacian http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13997 Patrizia Pucci, Mingqi Xiang and Binlin Zhang Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13998 Asymptotic stability and smooth Lyapunov functions for a class of abstract dynamical systems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13998 Michael Schönlein Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13999 Dacorogna-Moser theorem on the Jacobian determinant equation with control of support http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13999 Pedro Teixeira Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14000 Stability of Hasimoto solitons in energy space for a fourth order nonlinear Schrödinger type equation http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14000 Zhong Wang Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14001 Gradient estimates for the strong $p(x)$-Laplace equation http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14001 Chao Zhang, Xia Zhang and Shulin Zhou Sat, 1 Jul 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14002 Mathematical analysis of an <em>in vivo</em> model of mitochondrial swelling http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14002 Messoud A. Efendiev, Mitsuharu Ôtani and Hermann J. Eberl Sat, 1 Jul 2017 08:00:00 GMT