Showing papers in "Journal of Differential Equations in 2000"

TL;DR: In this article, the Sobolev space was established for the Camassa-Holm equation, and conditions on the initial data that lead to finite time blow-up of certain solutions were demonstrated.

TL;DR: In this paper, Wang and Zeng obtained multiple positive solutions of the nonlinear elliptic equation −h2 Δu+V(x) u=K(x), u|p−2 u+Q(x)) u, x∈RN, where V, K, Q are competing potential functions.

TL;DR: In this article, the authors obtained symmetry results of Gidas-Ni-Nirenberg type for cooperative nonlinear elliptic systems in the whole space, which is the same as the result of the present paper.

TL;DR: In this paper, a new approach for non-existence of positive solutions of cooperative semilinear elliptic systems with the Laplacian as principal part is introduced, based upon a new development of the method of moving spheres.

TL;DR: In this paper, the authors studied the p -system with frictional damping and showed that the solutions time-asymptotically tend to the nonlinear diffusion waves governed by the classical Darcy's law.

TL;DR: In this paper, the authors consider multi-peaked stationary solutions to the Cahn-Hilliard equation and prove their strong instability, justifying the name nuclei for the points of concentration.

TL;DR: In this article, the surface nucleation of superconductivity and the value of the upper critical field HC3 for superconductors occupying arbitrary bounded smooth domains in R3 were studied.

TL;DR: In this paper, the authors show that an entire large positive radial solution for the semilinear elliptic system Δu = p (|x |) v α, Δv = q (| x |) u β on R N, N ⩾3, for positive α and β, provided that the nonnegative functions p and q are continuous, c -positive, and satisfy the decay conditions ∫ ∞ 0 tp (t )−dt ∞ ∞ −tq ( t ) −t q (t) tq (

TL;DR: In this paper, a necessary condition and a sufficient condition for Cr robust permanence involving the average per-capita growth rates ∫ ǫ dμ with respect to invariant measures μ are derived.

TL;DR: In this paper, a model for the dynamics of a system of particles undergoing simultaneously coalescence and breakup is considered, each particle being assumed to be fully identified by its size, and the existence of solutions to the corresponding evolution integral partial differential equation is shown for product-type coagulation kernels with a weak fragmentation.

TL;DR: In this article, a delay differential equation with self-connections and two delays is considered, and conditions ensuring the stability of the periodic cycles are given in terms of local stability and bifurcation analysis.

TL;DR: In this paper, the authors studied the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type.

TL;DR: In this paper, a system of ODEs which describes the transmission dynamics of childhood diseases is considered, and a three-parameter unfolding of the normal form is studied to capture possible complex dynamics of the original system which is subjected to certain constraints on the state space due to biological considerations.

TL;DR: In this article, the authors give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1).

TL;DR: In this article, the convergence and consistency of approximate solutions derived by the modified Godunov scheme for the initial-boundary value problem to a simplified one-dimensional hydrodynamic model for semiconductors using the compensated compactness method was established.

TL;DR: In this article, the existence and uniqueness of global solutions to the mixed problem for the Carrier equation with acoustic boundary conditions were proved. But the authors did not consider the case where the boundary conditions are acoustic.

TL;DR: In this article, the authors proved that the number of limit cycles of a 3D competitive Lotka-Volterra system in R 3 + is finite if this system has not any heteroclinic polycycles.

TL;DR: The existence of the critical curve for p-q systems for nonlinear wave equations was already established by D. Del Santo, V. Georgiev, and E. Mitidieri.

TL;DR: In this article, the authors extend the Filippov-Wazewski theorem to the case when the state variable x is constrained to the closure of an open subset Θ⊂ R n.

TL;DR: In this paper, the authors studied the period function of the class of Hamiltonian systems where the origin is a non-degenerate center and showed that there are no nonlinear polynomial isochronous centers in this family.

TL;DR: In this article, the general principles by which certain structured population models or renewal equations can be reduced to ordinary differential equations or delay equations are systematically investigated with particular attention to retarded and neutral delay differential equations.

TL;DR: In this article, the authors considered the geometry of resonance tongues in reversible versions of Hill's equation, close to the classical Mathieu case, and proposed an averaging method, which enables a pull-back to the resonance tongues of the original system.

TL;DR: In this paper, the existence, stability, and multiplicity of coexistence states for a symbiotic Lotka-Volterra model with general diffusivities and transport effects are analyzed.

TL;DR: In this paper, the authors studied the following elliptic problem, where K(x) is a given function in Cα( R n\0) for some fixed α∈(0, 1), p>1 is a constant Some existence, monotonicity and asymptotic expansion at infinity of solutions of (*) are discussed

TL;DR: In this paper, the authors consider vector fields with a one-dimensional line of equilibria, and show that the Hopf-type loss of stability occurs in hyperbolic and elliptic vector fields.

TL;DR: In this article, the stability of the steady state solutions for an isentropic hydrodynamic model of semiconductors of two species was studied and shown to be asymptotically stable.

TL;DR: In this paper, the authors proved the existence of solutions for the sweeping process problem in the convex case, i.e., x(t)∈C(t), x(0)=x0∈ C(0), where C(.) is an arbitrary Hausdorff-Lipschitzean multifunction from I=[0, T] onto the set of nonempty closed subsets of R d.