Showing papers in "Journal of Differential Equations in 2011"

TL;DR: In this paper, a class of Kirchhoff type equations that involve sign-changing weight functions is examined and the existence of multiple positive solutions is established using the Nehari manifold and fibering map.

TL;DR: In this paper, the dynamics of a reaction-diffusion predator-prey system with strong Allee effect in the prey population is considered and nonexistence of nonconstant positive steady state solutions are identified.

TL;DR: In this paper, a diffusive logistic equation with a free boundary in higher space dimensions and a heterogeneous environment was studied, and the spreading-vanishing dichotomy established in Du and Lin (2010) [10] still holds in the more general and ecologically realistic setting considered here.

TL;DR: In this article, the authors obtained the global regularity for two partial dissipation cases and proved several global a priori bounds for two other prominent partial disipation cases involving the 2D Boussinesq equations.

TL;DR: In this paper, the Schrodinger-Poisson system (Pλ) with p∈(1,2) has a ground state if μ large and λ small.

TL;DR: The existence of random attractors for a large class of stochastic partial differential equations (SPDE) driven by general additive noise is established in this article, and bounds for the speed of attraction are obtained.

TL;DR: In this paper, it was shown that the Cauchy problem for the Novikov equation is locally well-posed in the Besov spaces B 2, r s with critical index s = 3 2.

TL;DR: In this article, the existence of global compact random attractors in weighted space l ρ 2 for stochastic lattice dynamical systems with random coupled coefficients and multiplicative/additive white noises was shown.

TL;DR: In this paper, the Yamabe equation Δ u + n (n − 2 ) 4 | u | 4 n − 2 u = 0 in R n, n ⩾ 3.

TL;DR: In this article, the authors investigated the mathematical theory of Hughes' model for the ow of pedestrians, consisting of a nonlinear conservation law for the density of pedestrians coupled with an eikonal equation for a potential modelling the common sense of the task.

TL;DR: In this article, global weighted L p estimates for the gradient of solutions to nonlinear elliptic Dirichlet boundary value problems over a bounded nonsmooth domain were obtained and the Morrey and Holder regularity of solutions were also established.

TL;DR: In this article, the authors established the existence and nonlinear stability of traveling wave solutions to a system of conservation laws which is transformed, by a change of variable, from the well-known Keller-Segel model describing cell (bacteria) movement toward the concentration gradient of the chemical that is consumed by the cells.

TL;DR: In this article, the global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces, using uniform estimates for a hyperbolic-parabolic linear system with convection terms.

TL;DR: For a strictly elliptic second order differential operator in divergence form with bounded, measurable coefficients on a Lipschitz domain, the authors showed that the parabolic problem with Robin or Wentzell-Robin boundary conditions is well-posed on C(Ω¯).

TL;DR: In this article, the authors studied the behavior of finite Morse index solutions of the equation − Δ u = | x | α | u | p − 1 u in Ω ⊂ R N, where p > 1, α > − 2, and Ω is a bounded or unbounded domain.

TL;DR: Nakanishi and Schlag as discussed by the authors studied the focusing, cubic, nonlinear Klein-Gordon equation in R 3 with large radial data in the energy space and gave a complete description of the evolution in that case.

TL;DR: In this article, the authors consider a set of nonlocal dispersal equations with bistable nonlinearity in one-dimensional spatial domain and characterize the asymptotic behaviors of the solutions as t → − ∞ in terms of appropriate subsolutions and supersolutions.

TL;DR: In this paper, the influence of the internal electric field on the qualitative behaviors of solutions is analyzed and it is shown that the electric field leads to the rotating phenomena in charge transport and reduces the speed of fluid motion, but it does not influence the transport of charge density and the heat diffusion.

TL;DR: In this article, the singular Weyl-Titchmarsh m-function of perturbed spherical Schrodinger operators (also known as Bessel operators) was investigated under the assumption that the perturbation q(x) satisfies xqx ∈ L1(0, 1).

TL;DR: In this article, the existence of random periodic solutions for semilinear stochastic differential equations was studied and the results were also valid for stationary solutions as a special case when the period τ can be an arbitrary number.

TL;DR: In this article, the Dirichlet-to-Neumann operator D 0 on a bounded open set Ω ⊂ R d whose boundary Γ has a finite (d − 1 ) -dimensional Hausdorff measure is defined by form methods.

TL;DR: In this paper, Chen and Zheng developed a direct approach to the problem to recover all the properties of the solutions obtained via the hodograph transformation of Li and Zheng (2009) [14].

TL;DR: In this article, the authors study fully non-linear elliptic equations in non-divergence form which can be degenerate when the gradient is small and establish an Alexandroff-Bakelman-Pucci estimate and prove a Harnack inequality for viscosity solutions of such degenerate elliptic problems.

TL;DR: In this paper, the authors prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n + k − 1 zeros counted with multiplicities.

TL;DR: In this article, the dispersive effect of the Coriolis force for the stationary and non-stationary Navier-Stokes equations is investigated and the existence of a unique solution is shown for arbitrary large external forces provided the coriolis forces is large enough.

TL;DR: In this article, a new iteration argument was introduced to get the sharp upper bound of the lifespan of solutions of semilinear wave equations in R4×[0,∞] with the initial data u(x, 0)=ef(x),ut(x and 0)=eg(x) of a small parameter e>0, compactly supported smooth functions f and g.

TL;DR: In this article, the authors show that the linear determinacy conjecture on the minimum wave speed is not true in general and show that it is identical to the asymptotical speed of population spread towards the stable equilibrium.

TL;DR: In this paper, the authors consider the defocusing energy-critical nonlinear Schrodinger equation of fourth order and prove that any finite energy solution is global and scatters both forward and backward in time in dimensions d ⩾ 9.

TL;DR: In this article, the authors address the question of well-posedness in spaces of analytic functions for the Cauchy problem for the hydrostatic incompressible Euler equations (inviscid primitive equations).

TL;DR: In this article, the boundary controllability of the Kuramoto-Sivashinsky equation is studied. Butler et al. used a Carleman estimate to obtain the null controllable trajectories of the nonlinear system.