Showing papers in "Nonlinear Analysis-theory Methods & Applications in 1988"
TL;DR: On etudie la regularite limite des solutions faibles de l'equation divA(x,u,Du)+B(x andu, Du) = 0 avec des conditions aux limites conormales et de Dirichlet.
Abstract: On etudie la regularite limite des solutions faibles de l'equation divA(x,u,Du)+B(x,u,Du)=0 avec des conditions aux limites conormales et de Dirichlet
1,278 citations
TL;DR: On formule plusieurs methodes de Galerkin a temps discret for des equations integrodifferentielles paraboliques as mentioned in this paper, a.k.a.
Abstract: On formule plusieurs methodes de Galerkin a temps discret pour des equations integrodifferentielles paraboliques
157 citations
TL;DR: In this article, a theorie dynamique generale generale for des problemes aux valeurs limites and initiales quasilineaires is proposed. But this theory is not a theory of dynamique.
Abstract: On etablit les fondements abstraits pour une theorie dynamique generale pour des problemes aux valeurs limites et initiales quasilineaires
126 citations
TL;DR: In this article, the authors give a mean value theorem for a lower semicontinuous function f on a Banach space, using the upper subderivatives defined by Rockafellar.
Abstract: THE PURPOSE of this paper is to give a mean value theorem for a lower semicontinuous function f on a Banach space, using the upper subderivatives defined by Rockafellar [l] As will be shown by example (Section 4), it may happen that the subdifferential af(x) is empty for all x in the closed line segment [a, 61, where a and b belong to X Therefore we cannot formulate the mean value theorem in such a form as that obtained in [2] and [3] for other generalized derivatives We prove among other factors that there exists a sequence (xk) converging to some point x E [a, 61, x # b, such that the sets df(xJ are nonempty and
90 citations
90 citations
TL;DR: In this article, the authors considered the case when there is only a single front, although multiple fronts may clearly occur, and provided detailed estimates for the error made by approximating the exact solution by the function constructed in Section 2.
Abstract: 4 = c2u, f(u, x)7 (1.1) is studied, where f is of bistable type for each x. Here “bistable” means that f vanishes for exactly three values of U, and fU is negative at the two outer ones; the prototype is f = u u3. When f is independent of x, the equation has a dynamical theory which is pretty well understood. Its most striking feature in that-case is the existence of travelling wave solutions, which are globally stable. This is also true for the heterogeneous equation (1. l), although such travelling wave solutions have up to now only been studied by formal asymptotics. They are not travelling waves in the strictest sense, but are rather frontal structures (confined to thin zones of width O(E)) which move with variable velocity. Starting with smooth arbitrary initial data Us which do not depend on E, the formation of these fronts at certain locations can be predicted, and their approximate subsequent motion can be determined by solving an ordinary differential equation. This heuristic analysis is explained in Section 2. The purpose of this paper is to provide the heuristics with a rigorous footing. In fact, we obtain detailed estimates for the error made by approximating the exact solution by the function constructed in Section 2. For simplicity, we treat the case when there is only a single front, although multiple fronts may clearly occur. The process under consideration consists of two parts, proceeding under two different time scales: which are the initial generation of a layer, followed by its propagation. The analysis describing the first part is the more involved. (If comparison functions based on the ordinary differential equation in Section 2 are used, the analysis simplifies, but weaker results are obtained.)
83 citations
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TL;DR: In this paper, a phenomene de trempe pour des non linearites non convex dans un espace de dimension arbitraire is demontre un phenomenomenon de trembe pour des convex non-linearites non-convex.
Abstract: On considere le probleme aux limites parabolique non lineaire suivant: u t −Δ u =f(u), t>0, x∈Ω, u=0, t>0, n∈∂Ω, u(0, x)=u 0 (x)≥0, x∈Ω. On demontre un phenomene de trempe pour des non linearites non convexes dans un espace de dimension arbitraire
79 citations
TL;DR: On donne des theoremes ergodiques non lineaires for des semigroupes commutatifs d'applications non dilatation without utiliser le concept de moyenne compacte as discussed by the authors.
Abstract: On donne des theoremes ergodiques non lineaires pour des semigroupes commutatifs d'applications non dilatation sans utiliser le concept de moyenne compacte
75 citations
TL;DR: On etablit l'existence des solutions positives de problemes a deux points limites singuliers pour des equations differentielles de la forme: y″+f(t,y,y')=o, o≤t≤1.
Abstract: On etablit l'existence des solutions positives de problemes a deux points limites singuliers pour des equations differentielles de la forme: y″+f(t,y,y')=o, o≤t≤1
71 citations
TL;DR: Soit Ω=R N -{0} (N∈N, N≥3) and soit V∈C 1 (RXΩ, R) as mentioned in this paper.
Abstract: Soit Ω=R N -{0} (N∈N, N≥3) et soit V∈C 1 (RXΩ, R). On etudie l'existence des solutions periodiques t→u(t)∈Ω, avec une periode prescrite, du systeme suivant de N equations differentielles d'ordre 2: u=−V'(t,u)
58 citations
TL;DR: On etudie le probleme aux valeurs limites periodiques pour un systeme d'equations differentielles d'ordre 2 faiblement couplees avec impulsion as mentioned in this paper.
Abstract: On etudie le probleme aux valeurs limites periodiques pour un systeme d'equations differentielles d'ordre 2 faiblement couplees avec impulsion
TL;DR: In this paper, Dirichlet et al. considered le probleme de Dirichelet pour l'equation elliptique semilineaire dans R N (N≥3) and considere le problem of Dirichele this paper :−Δu+u=Q(x)|u|γ 1 u, x∈R N, u∈H 1 (R N ), u¬=0, ou 1<γ<(N+2)/(N−2), Q(x) est une fonction
Abstract: On considere le probleme de Dirichlet pour l'equation elliptique semilineaire dans R N (N≥3):−Δu+u=Q(x)|u|γ 1 u, x∈R N , u∈H 1 (R N ), u¬=0, ou 1<γ<(N+2)/(N−2), Q(x) est une fonction positive, bornee et continue de Holder localement sur R N
TL;DR: On considere le probleme min x∈E F(x,λ) ou E est un espace de Hilbert reel, λ∈R et F:E×R→R est une fonctionnelle C 2
Abstract: On considere le probleme min x∈E F(x,λ) ou E est un espace de Hilbert reel, λ∈R et F:E×R→R est une fonctionnelle C 2
TL;DR: On considere la minimisation de l'integrale variationnelle ∫ G |⊇v| p dm(G⊂R n, 1
Abstract: On considere la minimisation de l'integrale variationnelle ∫ G |⊇v| p dm(G⊂R n , 1
TL;DR: On etudie le probleme de Cauchy pour l'equation de Hamilton-Jacobi u t +H(t, x, Du) = 0 dans (O, T)×R N avec la condition initiale u(o, x)=u o (x) pour x∈R N.
Abstract: On etudie le probleme de Cauchy pour l'equation de Hamilton-Jacobi u t +H(t, x, Du)=0 dans (O, T)×R N avec la condition initiale u(o, x)=u o (x) pour x∈R N . On a T>0, Hi [O, T]×R N ×R N →R et u o : R N →R sont donnes. On represente la solution viscosite comme la fonction valeur d'un jeu differentiel approprie
TL;DR: In this article, the authors et al. study the convergence of monotone fonctions in L 1 (a,b) equipe de la topologie de la convergence faible.
Abstract: On etudie les equations x(t)=f(t,x(t)) et x(t)=f(t,x(φ(t))) dans l'espace L 1 (a,b) equipe de la topologie de la convergence faible. On montre que ces equations ont des solutions integrables qui sont additionnellement des fonctions monotones p.p.
TL;DR: In this paper, a contre-exempleure complet a conjecture de Lazer et McKenna: si f: R→R est C 1, si f 1 (y)→μ(ν) quand y→∞(−∞), si ν<λ 1 <μ, si ξ∈σ(L) et si (ν, μ) contient au moins 2(k+1) valeurs propres de −Δ sur Ω, alors l'equation − Δu=f
Abstract: On donne un contre-exemple complet a une conjecture de Lazer et McKenna: si f: R→R est C 1 , si f 1 (y)→μ(ν) quand y→∞(−∞), si ν<λ 1 <μ, si ν∈σ(L) et si (ν, μ) contient au moins (k+1) valeurs propres de −Δ sur Ω, alors l'equation −Δu=f(u)−tφ 1 −v dans Ω, u=0 sur ∂Ω, a au moins 2(k+1) solutions pour t positif grand
TL;DR: In this paper, l'existence des solutions T-periodiques for des systemes hamiltoniens d'ordre 2 de la forme: −x=⊇V(x) ou V: R N −{0}→R est de classe C 2 et V(x)-→+∞ quand |x|→0
Abstract: On etudie l'existence des solutions T-periodiques pour des systemes hamiltoniens d'ordre 2 de la forme: −x=⊇V(x) ou V: R N −{0}→R est de classe C 2 et V(x)→+∞ quand |x|→0
TL;DR: In this article, the authors discuss le probleme aux valeurs limites et initiales suivant: u tt −u xx +|u t |α sign(u t )=0, (x,t)∈]0,1[χ]0.
Abstract: On considere le probleme aux valeurs limites et initiales suivant: u tt −u xx +|u t |α sign(u t )=0, (x,t)∈]0,1[χ]0,T]; u x (0,t)=g(t), u(1,t)=0, u(x,0)=u 0 (x), u t (x,0)=u 1 (x) avec 0<α<1. Avec u 0 ∈H 1 (]0,1[), u 1 dans L 2 (]0,1[) et g(t) dans L 2 (]0,T[) un theoreme d'existence globale et d'unicite est demontre
TL;DR: The authors decrit et on etudie des principes variationnels pour certaines classes d'equations operateur et de problemes aux valeurs initiales, et.
Abstract: On decrit et on etudie des principes variationnels pour certaines classes d'equations operateur et de problemes aux valeurs initiales
TL;DR: In this article, the authors introduce the notion of strongly efficient points for antisymmetric transitive relations and define the set of efficient points of an image A := f(D) of the constraint D. This relation is frequently referred to as preference.
Abstract: whenever, for every x E D such that A(x) afi(xO) for i = 1,2, . . . , n, one hash(x) = fi(x,,) for each i. Pareto optimization is also referred to as uecror, multi-objecfiue or multi-criteria optimization. Multi-objective maximization problems (0.1) have been nowadays extended to the situations where f is a mapping from X to a set Y equipped with a transitive relation 2. This relation is frequently called a preference. Consider first the image A := f(D) of the constraint D. An element y. of A is called (3_)-efficient (up to indifference or in the broad sense) if, for every y E A, y z y. implies y 5 yo; it is said to be strongly z-eficient (or efficient in the narrow sense) if, for each y E A, y 2 y. implies y = y,,. The two notions coincide for antisymmetric transitive relations. We shall be primarily concerned with efficient points in the broad sense. The set of efficient points of A (with respect to 7, ) will be denoted by max A (max Z A) and that of strongly efficient points, by max, A. An element of Y is called an efficient value of (0.1) if it is an efficient point of f(D). An element x0 of D is a solution of (0.1) if f(xo) is an efficient point of f(D). We shall use the latter S to denote the set of solutions of (0.1):
TL;DR: In this article, the authors define conditions tangentielles de type Nagumo, i.e., x'(t)+Ax(t)∈G(xC(H), x(o)=x 0 ∈K, ∀t∈[o,T], x(t]∈K ou A est un operateur elliptique and Kn'test pas necessairement compact.
Abstract: On etudie un probleme de la forme: x'(t)+Ax(t)∈G(xC(H), x(o)=x 0 ∈K, ∀t∈[o,T], x(t)∈K ou A est un operateur elliptique et K n'est pas necessairement compact. On trouve des conditions tangentielles de type Nagumo