Showing papers in "Journal of Differential Equations in 2004"

TL;DR: In this paper, an evolution equation with the regularized fractional derivative of an order α ∈ (0,1) with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables are considered.

TL;DR: In this article, the authors prove regularity theorems for minimizers of integral functionals of the Calculus of Variations with non-standard growth conditions of (p,q) type.

TL;DR: In this article, the authors present the classical maximum principle due to E. Hopf, together with an extended commentary and discussion of Hopf's paper, and discuss recent generalizations of the strong maximum principle, and also the compact support principle, for the case of singular quasilinear ellip-tic dierential inequalities, under generally weak assumptions on the quasILinear operators and the nonlinearities involved.

TL;DR: A topological technique for analyzing dynamical systems with complex behavior, based on the general notion of covering relations, which can be used to study multidimensional dynamical system with an arbitrary number of ‘topologically’ expanding directions.

TL;DR: In this article, the existence of an attractor for a 2D-Navier-Stokes system with delay is proved and the theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous.

TL;DR: In this article, the authors study a strongly coupled system of partial differential equations which models the dynamics of a two-predator-one-prey ecosystem in which the prey exercises a defense switching mechanism and the predators collaboratively take advantage of the prey's strategy.

TL;DR: In this paper, the authors considered the Dirichlet problem for positive solutions of the equation -Delta(m)(u) = f (u) in a bounded smooth domain Omega, with f locally Lipschitz continuous, and proved some regularity results for weak C-1( ) solutions.

TL;DR: In this article, the existence and nodal properties of four solutions for the p -Laplacian equation on a bounded domain Ω⊂ R N with smooth boundary ∂Ω provided that the nonlinearity f is superlinear and subcritical and the equation has a pair of subsolution and supersolution.

TL;DR: In this paper, the existence, multiplicity and nonexistence of positive ω-periodic solutions for the periodic equation x′(t)=a(t)g(x)x (t)−λb(t),f(x(t−τ(t))) were investigated.

TL;DR: In this paper, the authors answer affirmatively an open problem (cf. Theorem 4′ in Ferrero and Gazzola (J. Differential Equations 177 (2001) 494): if Ω∋0 is an open-bounded domain, Ω⊂R N (N⩾5) and assume that 0⩽μ N−2 2 ) 2 −( N+2 N ) 2, then, for all λ>0 there exists a nontrivial solution with critical level in the range (0, 1

TL;DR: The existence of periodic relaxation oscillations in singularly perturbed systems with two slow and one fast variable is analyzed geometrically in this article, where it is shown that near a singular periodic orbit a return map can be defined which has a one-dimensional slow manifold with a stable invariant foliation.

TL;DR: In this article, the authors demonstrate some special behavior of steady-state solutions to a predator-prey model due to the introduction of spatial heterogeneity, and they show that positive steadystate solutions with certain prescribed spatial patterns can be obtained when the spatial environment is designed suitably.

TL;DR: In this paper, it was shown that the solution of the linear damped wave equation asymptotically decomposes into a solution of heat and wave equations and the difference of those solutions satisfies the Lp−Lq type estimate.

TL;DR: In this article, the existence of positive solutions for a nonlinear Dirichlet problem involving the m -Laplacian was studied, and a blow-up argument and a Liouville-type theorem were used to obtain a priori estimates.

TL;DR: In this paper, the authors studied the multiple existence of positive solutions for the following strongly coupled elliptic system, where α,β,a,b,c,d are positive constants and Ω is a bounded domain in R N.

TL;DR: In this paper, the authors prove the existence and uniform decay rates of the energy by assuming a nonlinear feedback β(ut) acting on the boundary provided that β has necessarily not a polynomial growth near the origin.

TL;DR: The existence of singular solutions of the incompressible Navier-Stokes system with singular external forces, the existence of regular solutions for more regular forces as well as the asymptotic stability of small solutions (including stationary ones), and a pointwise loss of smoothness for solutions are proved in the same function space of pseudomeasure type as discussed by the authors.

TL;DR: In this article, the convergence of solution to the Cahn-Hilliard equation to an equilibrium as time goes to infinity has been proved, and the existence of global attractor and maximal regularity of solution have been obtained.

TL;DR: In this paper, a linearized model for fluid-structure interaction in one space dimension is considered and a spectral asymptotic analysis on high frequencies for the underlying semigroup is presented, showing that the semigroup governed by the system can be split into a parabolic and a hyperbolic projection.

TL;DR: In this paper, the authors studied smoothing properties for time-dependent Schrodinger equations with potentials which satisfy O(|x|m) at infinity, m⩾2.

TL;DR: In this article, a sufficient condition for the existence of a global attractor for general lattice dynamical systems is presented, and the existence and approximation of an attractor is investigated for second-order and first-order lattice systems.

TL;DR: In this article, the existence and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks is studied. But, the authors do not apply in solving these problems because there is no maximum principle or conservation laws available to the integral differential equation.

TL;DR: In this paper, the authors obtained the continuity of attractors for semilinear parabolic problems with Neumann boundary conditions relatively to perturbations of the domain, and gave necessary and sufficient conditions for the spectral convergence of Neumann problems under perturbation.

TL;DR: In this paper, the authors considered the heat equation with a source term localized in a Riemannian manifold, and showed that the initial data can be steered to 0 in an arbitrarily small time by applying a suitable control in the control region.

TL;DR: In this paper, pointwise estimates for the kernels associated to the polyharmonic Dirichlet problem on bounded smooth domains were derived, and optimal weighted L p -L q -regularity estimates for weights involving the distance function were obtained.

TL;DR: In this paper, the stability analysis for coexistence steady-state solutions obtained by Kuto and Yamada is discussed and the Hopf bifurcation phenomenon occurs on the stable-state solution branch under some conditions.

TL;DR: In this article, the authors studied the full-time dynamics of the initial value problem, for u e = u e ( x, t ), u t e = e 2 u xx e - F ǫ ( u e ), x ∈ R, t > 0, u e( x, 0 ) = u 0 ( x ), x∈ R, where 0 e ⪡ 1 and F ( u ) has global minimum 0 at u = ± 1.

TL;DR: In this paper, the abstract parabolic evolutionary equations are analyzed in continuous interpolation spaces allowing a singularity as t↓0,2 where Dtα denotes the time-derivative of order α∈(0, 2).

TL;DR: In this paper, the authors studied the existence of nontrivial solutions of the concave-convex problem with 1