Showing papers in "Journal of Differential Equations in 1996"

TL;DR: In this paper, the authors proposed a mathematical model for spatial segregation of interacting species, where u1 and u2 represent the densities of two competing species, d1 and d2 are their diffu- sion rates, a1 and a2 denote the intrinsic growth rates, b1 and c2 account for intra specific competitions, b2 and c1 are the coefficients of inter-specific competitions, :11 and :22 are usually referred as selfdiffusion pressures, and :12 and :21 are cross-diffusion pressure.

TL;DR: In this article, the Poincare-Bendixson theorem holds for cyclic nearest neighbor systems of differential delay equations, in which the coupling between neighbors possesses a monotonicity property.

TL;DR: In this paper, the authors prove the L 1 -contraction principle and uniqueness of solutions for quasilinear elliptic-parabolic equations of the form[formula] where b is monotone nondecreasing and continuous.

TL;DR: In this article, the existence and uniqueness of principal eigenvalues for some linear weighted boundary value problems associated to a general second order uniformly elliptic operator were studied. But the problem was not addressed in this paper.

TL;DR: In this paper, a discrete (integer-valued) Lyapunov function V for cyclic nearest neighbor systems of differential delay equations possessing a feedback condition was defined, and the values of V were derived from the real parts of the Floquet multipliers for such linear periodic systems.

TL;DR: In this paper, the authors studied the asymptotic behavior of the solutions to evolution equations of the form 0 # u* (t)+f(u(t), =(t)); u(0)=u0, where [f (}, =): =>0] is a family of strictly convex functions whose minimum is attained at a unique point x(=).

TL;DR: In this paper, the authors derived a result on the limit of certain sequences of principal eigenvalues associated with some elliptic eigenvalue problems, and used this result to give a complete description of the global structure of the curves of positive steady states of a parameter dependent diffusive version of the classical logistic equation.

TL;DR: In this paper, the first bifurcation that needs to be addressed concerns the existence, uniqueness and stability of a feasible (non-negative) equilibrium for Dirichlet conditions.

TL;DR: In this paper, the authors derived a neutral difference-differential system with diffusion which arises from a ring array of coupled lossless transmission lines and applied a global Hopf bifurcation theorem to establish the existence of multiple large amplitude phase-locked periodic solutions in the corresponding neutral system.

TL;DR: In this article, the problem of finding spiky solutions of (1.1) has been studied in various applications, such as chemotaxis, population genetics, and chemical reactor theory.

TL;DR: In this paper, an expression for the derivative of an eigenvalue with respect to a given parameter: an endpoint, a boundary condition, a coefficient or the weight function is found.

TL;DR: In this article, the authors show how an ordinary differential equation admitting SL(2) as a symmetry group can be reduced in order by three, and the solution recovered from that of the reduced equation via a pair of quadratures and a linear second order equation.

TL;DR: The viscous Cahn-Hilliard equation as mentioned in this paper is a singular limit of phase field equations for phase transitions, and it can be formulated as a one-parameter homotopy connecting the Cahn−Hilliard (α = 0) and Allen-Cahn (α=1) models.

TL;DR: In this paper, existence criteria are established for singular boundary value problems for nonlinear second order ordinary and delay differential equations, and theorems obtained are very general and complement previous known results.

TL;DR: In this paper, a coupled system of ODE for growing, interacting sand cones is studied and it is shown that these ODE correspond to the evolution inL2generated by the subdifferential of the convex functional which vanishes on functions whose gradient has length less than or equal to one and is infinity otherwise.

TL;DR: In this paper, the asymptotic behavior of the flow for a system of the Navier-Stokes type is investigated and the existence of a global attractor with a finite fractal dimension is proved.

TL;DR: In this paper, an idea of quasi-homogeneous normal form theory using new grading functions is introduced, the definition of Nth order normal form is given and some sufficient conditions for the uniqueness of normal forms are derived.

TL;DR: In this paper, a new method to determine the monotonicity of the ratio of two Abelian integrals is given, based on two criterion functions defined directly by the functions which appear in the Abelian Integrals.

TL;DR: In this paper, periodic solution operators for the equation Δu+2iζ·∇u=fin a bounded domain with the help of Fourier series were constructed and proved that the L 2 norm of these operators converge to zero if the parameter |Im ǫ| goes to infinity.

TL;DR: In this article, the singular behavior of variational nonlinear wave solutions with cusp singularities has been analyzed, and it has been shown that constant solutions of the equation are nonlinearly unstable.

TL;DR: In this article, an explicit procedure to establish upper bounds for the number of real zeros of analytic functions satisfying linear ODEs with meromorphic coefficients was proposed. But this procedure requires the existence of singular points in a small neighborhood of a real segment, and all the coefficients have absolute value ⩽AonUanda0(t)≡1.

TL;DR: In this paper, the existence of global solutions for large data for a class of systems of thermoelastic type with non-local nonlinearities was studied, and the Decay rates of Sobolev norms of the solutions as time tends to infinity were investigated.

TL;DR: In this article, the one-dimensional wave equation with damping of indefinite sign in a bounded interval with Dirichlet boundary conditions is considered and it is proved that solutions decay uniformly exponentially to zero provided the damping potential is in the BV-class, has positive average, is small enough and satisfies a finite number of further constraints guaranteeing that the derivative of the real part of the eigenvalues is negative when the dampings vanishes.