Showing papers in "Journal of Differential Equations in 1989"

TL;DR: In this article, Dirichlet suivant considered the problem: (O p (u'))'+f(t,u)= 0, u(0)=u(T)=0, ou T est un nombre reel positif

TL;DR: In this paper, the authors studied the large-time behavior of solutions to the initial-value problem for the Korteweg-de Vries equation and for the regularized long-wave equation, with a dissipative term appended.

TL;DR: In this paper, the authors consider the initial value problem for the semilinear heat equation and show that each solution possesses an "asymptotic profile" in a certain sense and tends to this profile as time increases.

TL;DR: In this paper, an n -degrees of freedom Hamiltonian system near an elliptic equilibrium point is considered, and the system is put in normal form (up to an arbitrary order and with respect to some resonance module) and estimates are obtained for both the size of the remainder and for the domain of convergence of the transformation leading to normal form.

TL;DR: In this article, the boundary value problem is studied under conditions which are modeled on the problem y″ + a(x)y−p = 0y(0) = y(1) = 0 or y′(0), where y is the number of cones.

TL;DR: In this paper, the authors propose an equation d'evolution which en resulte: u˙+(1+|Du| 2 ) 1'2 •Au=0 dans Ω+[0,T]

TL;DR: On considere les proprietes spectrales du probleme differentiel, l(f)=(−1) n (p 0 f (n) ) (n)) +(− 1) n−1 (p 1 f n − 1 (n − 1) +p n f =λrf sur un intervalle fini ou infini (a,b) avec des coefficients reels localement sommables 1/p 0,p 1,p n,r sous l'hypothese que p 0 > 0 and que la f

TL;DR: In this article, the authors present an existence and a stability proof for solutions to the BGK model of Boltzmann Equation δ,f+v·▽ x f+f=M[f], t⩽0,x∈ R N,v∈ r N M[f]=( p (2φT) N 2 ) exp ( −|v−u| 2 2T ), (p,pu,p|u|2 +pT)(1,x)=∞ R N (1,v,

TL;DR: In this paper, the authors studied the local solvability of a general non-classical parabolic equation via an auxiliary problem and the Schauder fixed point principle and derived a priori estimates to establish the global existence of the solution.

TL;DR: In this paper, a nouvelle theorie appelee le developpement exponentiel et explore ses interactions avec la theorie de la variete invariante locale, les λ-lemmes et la theory de linerarisation reguliere.

TL;DR: In this paper, the authors proved the long-time existence of the flow in Q(H) for the nonlinear Schrodinger equation in R n i ∂ψ ∂t = − 1 2 Δψ + Vψ − ¦ψ¦ p−1 ψ, 1 ⩽p 4 n, where the potential V is bounded below and satisfies the condition that ¦D α V¦ is bounded for all ¦α¦ ⩾ 2.

TL;DR: In this paper, the authors considered second order in time equations of Petrovsky type (wave and plate-like) with nonlinear dissipative boundary conditions and established the results on asymptotic behavior of the solutions.

TL;DR: The main purpose of as mentioned in this paper is to prove that if W ϵ C α (Ω) is a small perturbation of P in Ω, then max W (x) > 0 (min W(x) 0 (t− u + u + (u − ) ~ G P Ω outside a compact set in a domain Ω ⊆ R n.

TL;DR: On considere l'existence de solutions 2Π-periodiques des systemes hamiltoniens asymptotiquement quadratiques −Jz=H'(z,t) ou J=(0―I/I#0), I=In, la matrice identite de n×n

TL;DR: The concept of stability radius for time-varying linear systems is introduced and Invariance properties of the stability radius are analysed for the group of Bohl transformations.

TL;DR: In this article, the authors consider des equations paraboliques semi-lineaires: dy/dt+Ay=f(y), ou A est un operateur sectoriel sur un Banach X ayant une resolvante compacte and f est une C 2 -application de l'espace des puissances fractionnaires Xα, 0≤α<1, dans X. Alors il existe an voisinage U de y 0 =y(0) avec la propriete suivante: si z∈U\

TL;DR: In this article, a caracterisation elaboree des comportements des fonctions propres du laplacien avec la condition limite de Neumann.

TL;DR: In this article, the robustness of stable linear systems is examined and the smallest perturbation which destroys stability is determined, where the perturbations are assumed to have unbounded structure.

TL;DR: For 3D systems that are competitive or cooperative, this article presented new criteria for existence of equilibria and cycles, convergence of all trajectories, global stability, and structural stability.

TL;DR: In this paper, Cartan's equivalence method is used to study the differential invariants of a single second order ordinary differential equation relative to the pseudo-group of point transformations, and a simple characterization is given of those second order equations which are linearizable by a point transformation.

TL;DR: In this article, the authors considered the nonlinear Hill's equation with periodic forcing term and proved that all solutions of the above-mentioned equation are bounded for t ϵ R and that there are infinitely many quasi-periodic solutions and an infinity of periodic solutions of minimal period m, for each positive integer m.

TL;DR: Soit R + n ={(x 1,x 2,…,x n−1,x n ); x n > 0} (n≥ 2) on considere les equations de Navier-Stokes.

TL;DR: In this paper, the saddle point theorem is extended to the case of functions defined on a product space X × V, where X is a Banach space and V is a compact manifold.

TL;DR: The authors construit des formes canoniques for tous les champs vectoriels en equilibre a 0∈R n relativement au groupe des diffeomorphismes formels (resp. des transformations canoniques) tangentiels a l'identite.

TL;DR: In this article, the authors discuss the existence of nontrivial solutions of the Dirichlet problem in a bounded domain in RN (N ⩾ 2) with smooth boundary ∂Ω and discuss the position of the point (p−, p+) in the plane with the extended spectrum of −Δ.

TL;DR: On etudie l'existence de la solution non constante bornee de l'equation differentielle ΔW-y ⊇W/2+/W/P−1 -W -W/(p-1)=0 dans R n, n2 avec pp c ou P c =(n+2)/(n-2) est l'exposant de l'sespace de Sobolev critique for R n.

TL;DR: In this article, an inertial manifold is constructed for the scalar reaction-diffusion equation u t = vu xx +ƒ(u) with a cubic nonlinearity, and uniform bounds for the number of zeros along solutions to the variational equations satisfied by the difference of two elements on the unstable manifolds of equilibria.

TL;DR: In this paper, a family of polynomial vector fields with three limit cycles appearing simultaneously on a Hopf bifurcation (H) of order 3 and vanishing simultaneously in a homoclinic loop bifurancation (HL) was presented.

TL;DR: In this article, the authors make the connection between the theoretical study of the generalized homoclinic loop bifurcation (GHB ∗ ) and the practical computational aspects, and calculate saddle quantities for quadratic systems, and deduce a bound for the number of limit cycles that appear in a GHB ∆.