Showing papers in "Journal of Differential Equations in 2013"

TL;DR: In this paper, the existence and multiplicity of solutions for elliptic equations in R N, driven by a non-local integro-differential operator, which main prototype is the fractional Laplacian, was studied.

TL;DR: In this article, the authors established temporal decay estimates for weak solutions to the Hall-magnetohydrodynamic equations and obtained algebraic time decay for higher order Sobolev norms of small initial data solutions.

TL;DR: In this paper, the existence of nontrivial solution and concentration results are obtained via variational methods under suitable assumptions on V and K. In particular, the potential V is allowed to be sign-changing for the case p ∈ ( 4, 6 ).

TL;DR: In this article, the quasilinear Schrodinger equation is considered and the authors employ the approach developed in Szulkin and Weth (2009, 2010) [15], [16] and obtain infinitely many geometrically distinct solutions.

TL;DR: In this paper, the sharp local singular Adams inequality was shown to hold on high order Sobolev spaces W m, n m (R n ) of arbitrary integer order m (Theorem 1.1) which improved the results of Ruf and Sani [48] where sharp Adams inequalities were established for even m and those of the authors (Lam and Lu, 2012 [28], [29] ) for odd m but with different and more restricted norms.

TL;DR: In this paper, the authors established global existence and uniqueness for the two-dimensional non-diffusive Boussinesq system with anisotropic viscosity acting only in the horizontal direction, which arises in ocean dynamics models.

TL;DR: In this paper, the authors studied the global regularity of 2D incompressible magnetohydrodynamic (MHD) equations with horizontal dissipation and horizontal magnetic diffusion and showed that the horizontal component of any solution admits a global (in time) bound in any Lebesgue space L2r with 1⩽r<∞ and the bound grows no faster than the order of rlogr as r increases.

TL;DR: In this article, the existence of a positive ground state solution for the following class of elliptic equations was investigated: Δ u + V (x ) u = K ( x ) f ( u ) in R N, where N ⩾ 3, V, K are nonnegative continuous functions and f is a continuous function with a quasicritical growth.

TL;DR: In this article, the authors proved the global existence of strong solution with vacuum to the 2D nonhomogeneous incompressible Navier-Stokes equations, as long as the initial data satisfies some compatibility condition.

TL;DR: In this paper, a perturbation approach is used to treat the critical exponent case giving new existence results for a class of quasilinear Schrodinger equations which include the Modified Nonlinear Schrodings.

TL;DR: In this article, the authors studied the Cauchy problem for abstract dissipative equations in Hilbert spaces generalizing wave equations with strong damping terms in R N or exterior domains.

TL;DR: In this paper, the L p -Minkowski problem was studied for p = − n − 1, which corresponds to the critical exponent in the Blaschke-Santalo inequality.

TL;DR: In this article, the authors studied the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are − ν ( − △ ) α u and − κ ( − ǫ ) β b, and showed that smooth solutions are global in the following three cases: α ≥ 1/2, β ≥ 1 ; 0 ≤ α 1 /2, 2 α + β > 2 ; α ≥ 2, β = 0.

TL;DR: In this article, the existence of a martingale solution for the stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise is proved.

TL;DR: In this article, the authors present a KAM theory for dissipative systems with n degrees of freedom depending on n parameters, and show that it is possible to find solutions with a fixed n-dimensional (Diophantine) frequency by adjusting the parameters.

TL;DR: In this paper, the existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying local monotonicity and generalized coercivity conditions was established, and an analogous result was obtained for stochastic evolution equations in Hilbert space with additive noise.

TL;DR: In this paper, the authors consider the monomial weight | x 1 | A 1 ⋯ | x n | A n in R n, where A i ⩾ 0 is a real number for each i = 1, …, n, and establish Sobolev, isoperimetric, Morrey, and Trudinger inequalities involving this weight.

TL;DR: In this article, the authors considered the modified Camassa-Holm equation with cubic nonlinearity, which is integrable and admits the single peaked solitons and multi-peakon solutions.

TL;DR: In this article, the authors considered the time periodic Lotka-Volterra competition-diffusion system and proved that the traveling wave solution is asymptotically stable and unique modulo translation for frontlike initial values.

TL;DR: In this paper, the authors established the nonlinear stability of traveling wave solutions to a chemotaxis model with singular (or logarithmic) sensitivity and its transformed parabolic hyperbolic system.

TL;DR: In this paper, the authors considered a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of the power and showed that for some values of the parameters the equation does not have nontrivial nonnegative supersolutions in exterior domains.

TL;DR: In this paper, the authors present an asymptotic formation of phase-locked states from the ensemble of Kuramoto oscillators with a symmetric and connected interaction topology, and derive the uniform boundedness of fluctuations using Łojasiewicz gradient inequality.

TL;DR: In this paper, a formula for computing the slow divergence integrals for predator-prey systems with response functions of Holling types was developed, and it was shown that the cyclicity of any limit periodic set is at most two, that is, two families of hyperbolic limit cycles or at most one family of limit cycles with multiplicity two can bifurcate from the limit periodic sets by small perturbations.

TL;DR: In this article, the combined effects of dispersal and spatial variations on the outcome of the competition were investigated using the Lotka-Volterra competition system, and it was shown that a heterogeneous distribution of resources is usually superior to its homogeneous counterpart in the presence of diffusion.

TL;DR: In this paper, the Cauchy problem for linear partial differential equations of non-Kowalevskian type in the complex domain is considered and the precise bound of the admissible order of entire functions is described in terms of the Newton polygon of the equation.

TL;DR: In this paper, the Calderon-Zygmund theory for a nonlinear parabolic equation of p-Laplacian type in divergence form was shown to hold for every q ∈ [1, ∞] for every (x,t)-variant.

TL;DR: In this article, it was shown that the global attractor is the union of all the bounded complete trajectories which are strong solutions in two dimensions, provided that the potential is real analytic and the external forces vanish.

TL;DR: In this paper, the authors investigated the spectral properties of the 1-D Dirac differential expression with point interactions on a discrete set and showed that certain spectral properties (self-adjointness, discreteness, absolutely continuous and singular spectra) of the realizations of these realizations correlate with the corresponding spectral properties on the Jacobi matrices B X, α and B X, β, respectively.

TL;DR: For evolutionary p-Laplacian systems in the setting of Lorentz spaces, the Calderon-Zygmund type was proved in this paper for mutatis mutandis.