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961.
Thierry Cazenave Daoyuan Fang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2011,28(1):135
For the nonlinear Schrödinger equation iut+Δu+λα|u|u=0 in RN, local existence of solutions in Hs is well known in the Hs-subcritical and critical cases 0<α?4/(N−2s), where 0<s<min{N/2,1}. However, even though the solution is constructed by a fixed-point technique, continuous dependence in Hs does not follow from the contraction mapping argument. In this paper, we show that the solution depends continuously on the initial value in the sense that the local flow is continuous Hs→Hs. If, in addition, α?1 then the flow is locally Lipschitz. 相似文献
962.
Constrained diffusions, with diffusion matrix scaled by small ?>0, in a convex polyhedral cone G⊂Rk, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B⊂G be a bounded domain. Under conditions, an “exponential leveling” property that says that, as ?→0, the moments of functionals of exit location from B, corresponding to distinct initial conditions, coalesce asymptotically at an exponential rate, is established. It is shown that, with appropriate conditions, difference of moments of a typical exit time functional with a sub-logarithmic growth, for distinct initial conditions in suitable compact subsets of B, is asymptotically bounded. Furthermore, as initial conditions approach 0 at a rate ?2 these moments are shown to asymptotically coalesce at an exponential rate. 相似文献
963.
We develop an idea of Evans and O’Connell (1994) [13], Engländer and Pinsky (1999) [10] and Duquesne and Winkel (2007) [4] by giving a pathwise construction of the so-called ‘backbone’ decomposition for supercritical superprocesses. Our results also complement a related result for critical (1+β)-superprocesses given in Etheridge and Williams (2003) [11]. Our approach relies heavily on the use of Dynkin-Kuznetsov N-measures. 相似文献
964.
Joseph F. Grcar 《Historia Mathematica》2011,38(2):163-218
Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method — which Euler did not recommend, which Legendre called “ordinary,” and which Gauss called “common” — is now named after Gauss: “Gaussian” elimination. Gauss’s name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least-squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices. 相似文献
965.
The paper deals with the classical Caristi fixed point theorem in vector valued metric spaces. The results obtained seem to be new in this setting. 相似文献
966.
Lenka Hal?inová Radko Mesiar 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(5):1545-1554
In this paper we continue the study of a submeasure notion introduced in Hutník and Mesiar (2009) [1] involving a class of operations which provides a generalization ofτT-submeasures. We construct pseudo-metrics and metrics generated by such probabilistic submeasures. Two possible generalizations of our submeasure notion are discussed. 相似文献
967.
968.
Valeri Obukhovskii Pietro Zecca 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(8):2765-2777
We introduce the notion of a multivalued causal operator and consider an abstract Cauchy problem in a Banach space for various classes of functional inclusions with causal operators. The methods of the topological degree theory for condensing maps are applied to obtain local and global existence results for this problem and to study the continuous dependence of a solution set on initial data. As application we generalize some existence results for semilinear functional differential inclusions and Volterra integro-differential inclusions with delay. 相似文献
969.
970.
Jayne Thompson 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(15):4989-4999
We establish stability and nonstability results for a domain-wall brane model arising in classical field theory. In particular, we show the nonexistence of nontrivial bounded solutions on the real line for a coupled pair of parameter dependent linear second order ordinary differential equations for an open set of those parameters. Moreover, we establish the existence of nontrivial solutions for a hypersurface of the parameters. We use Fredholm theory for compact linear operators combined with the Lyapunov-Schmidt method to prove our results. The model is stable, respectively unstable, for those parameters for which the coupled system does not, respectively does, have nontrivial solutions. 相似文献