Showing papers in "Journal of Differential Equations in 2009"

TL;DR: In this article, the existence of multiple spatially non-homogeneous periodic orbits while the system parameters are all spatially homogeneous is investigated. But the results are limited to the case where the system is a diffusive predator-prey system with Holling type-II predator functional response subject to Neumann boundary conditions.

TL;DR: The existence of a pullback attractor for a stochastic reaction-diffusion equation on all n-dimensional space has been established in this paper, where the reaction is recast as a random dynamical system and asymptotic compactness for this is demonstrated by using uniform a priori estimates for far-field values of solutions.

TL;DR: In this article, Pejsachowicz et al. formulated general second order quasilinear elliptic systems with nonlinear boundary conditions on bounded domains into nonlinear mappings between Sobolev spaces and showed that the linearized mapping is a Fredholm operator of index zero.

TL;DR: In this article, the authors construct small-amplitude steady periodic water waves with constant vorticity, which do not exist in the irrotational setting, and give a full description of the particle paths.

TL;DR: In this paper, a reaction-diffusion population model with a general time-delayed growth rate per capita is considered, and the stability of the positive steady state solution and the existence of forward Hopf bifurcation from the positive stable state solution are obtained via the implicit function theorem.

TL;DR: In this article, the authors studied the asymptotic behavior of the endemic equilibrium as the diffusion rate of the susceptible individuals goes to zero in the case where a so-called low-risk subhabitat is created.

TL;DR: In this paper, Ekeland variational principle, mountain pass theorem and a suitable Trudinger-Moser inequality are employed to establish sufficient conditions for the existence of solutions of quasilinear nonhomogeneous elliptic partial differential equations of the form − Δ N u + V (x ) | u | N − 2 u = f ( x, u ) + e h ( x ) in R N, N ⩾ 2, where V : R N → R is a continuous potential.

TL;DR: In this paper, a class of time-delayed reaction-diffusion equations with local nonlinearity for the birth rate was studied and the authors showed that these wavefronts are asymptotically stable, when the initial perturbation around the traveling waves decays exponentially as x → − ∞, but the original perturbations can be arbitrarily large in other locations.

TL;DR: In this paper, an initial and boundary value problem for the Korteweg-de Vries equation on a bounded interval with nonhomogeneous boundary conditions is studied, where the boundary value is a function of the initial value.

TL;DR: The existence of a compact random attractor for the stochastic Benjamin-Bona-Mahony equation defined on an unbounded domain was proved in this article, which is invariant and attracts every pulled-back tempered random set under the forward flow.

TL;DR: In this article, sufficient conditions for the existence of integral solutions and extremal integral solutions for some nondensely defined impulsive semilinear functional differential inclusions in separable Banach spaces are established.

TL;DR: In this article, the existence, multiplicity and concentration of positive solutions for the following class of quasilinear problems were studied, where Δ N u is the N-Laplacian operator, ϵ is a positive parameter, N ⩾ 2, V : R N → R is a continuous function and f : R → R was a C 1 function having critical exponential growth.

TL;DR: In this paper, the principal eigenvalue λ 1 ( Ω ) of the nonlocal Dirichlet problem (J ∗ u ) (x ) − u (x) = − λ u ( x ) in R N ∖ Ω with u( x ) = 0 in R n ∖

TL;DR: In this paper, the authors considered the diffusive Leslie predator-prey model with large intrinsic predator growth rate, and investigated the change of behavior of the model when a simple protection zone Ω 0 for the prey is introduced.

TL;DR: In this article, a planar cubic system with at least 13 limit cycles was constructed based on counting the number of zeros of some Abelian integrals, and the construction was proved to have at least 14 limit cycles.

TL;DR: In this paper, it was shown that elliptic second order operators of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth, the coefficients of A are discontinuous and A is complemented with mixed boundary conditions.

TL;DR: In this article, the authors improved the Darboux theory of integrability with multiplicity by taking into account the multiplicity of the invariant algebraic hypersurfaces.

TL;DR: In this article, a geometric framework for the steady-state PNP system involving multiple types of ion species with multiple regions of piecewise constant permanent charge is provided, which together with the general framework allows one to reduce the existence and multiplicity of singular orbits to a system of nonlinear algebraic equations.

TL;DR: In this article, the focusing energy-critical nonlinear Schrodinger equation of fourth order iut+Δ2u=|u|8d−4u, d⩾5.

TL;DR: In this article, it was shown that there still exist the critical global existence exponent and the critical Fujita exponent for pseudo-parabolic equations and these two critical exponents are consistent with the corresponding semilinear heat equations.

TL;DR: In this paper, the convergence of solutions to equilibria for quasilinear parabolic evolution equations in situations where the set of equilibrium is non-discrete, but forms a finite-dimensional C 1 -manifold which is normally hyperbolic.

TL;DR: In this article, the existence and uniqueness of energy solutions in the case where the growth exponent of the non-linearity ϕ is less than 6 and f may have arbitrary polynomial growth rate.

TL;DR: In this paper, the authors show that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies, and the C 2, 1 regularity of the value function is proven.

TL;DR: In this article, the stable manifold theorem for hyperbolic fixed points of a map has been shown to hold for covering relations with cone conditions, and a new geometric proof of the theorem has been given.

TL;DR: In this paper, the non-existence of non-constant positive steady state solutions of two reaction-diffusion predator-prey models with Holling type-II functional response when the interaction between the predator and the prey is strong is proved.

TL;DR: In this paper, the existence and uniqueness of the strong solution of the Navier-Stokes-Poisson system is shown in the framework of hybrid Besov spaces in three and higher dimensions.

TL;DR: In this article, the existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient was studied.

TL;DR: In this article, the existence of solutions of the Dirichlet problem if both principal eigenvalues are negative, provided the second eigenvalue is positive, and generalize the anti-maximum principle for second-order elliptic operators to homogeneous, fully nonlinear operators.

TL;DR: In this paper, the authors give the definition of random periodic solutions of random dynamical systems and prove the existence of such periodic solutions for a C 1 perfect cocycle on a cylinder using a random invariant set.