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991.
992.
Antoine Gloria Stefan Neukamm 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2011,28(6):941
We prove under some general assumptions on elastic energy densities (namely, frame indifference, minimality at identity, non-degeneracy and existence of a quadratic expansion at identity) that homogenization and linearization commute at identity. This generalizes a recent result by S. Müller and the second author by dropping their assumption of periodicity. As a first application, we extend their Γ-convergence commutation diagram for linearization and homogenization to the stochastic setting under standard growth conditions. As a second application, we prove that the Γ-closure is local at identity for this class of energy densities. 相似文献
993.
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
994.
995.
Ioan I. Vrabie 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7047-7060
In this paper, we prove a sufficient condition for the global existence of bounded C0-solutions for a class of nonlinear functional differential evolution equation of the form where X is a real Banach space, A is the infinitesimal generator of a nonlinear compact semigroup, is a nonempty, convex, weakly compact valued, and almost strongly–weakly u.s.c. multi-function, and is nonexpansive. 相似文献
996.
Bo Göran Johansson 《Historia Mathematica》2011,38(3):338-367
The algorithms used in Arabic and medieval European mathematics for extracting cube roots are studied with respect to algebraic structure and use of external memory (dust board, table, paper). They can be separated into two distinct groups. One contains methods used in the eastern regions from the 11th century, closely connected to Chinese techniques, and very uniform in structure. The other group, showing much wider variation, contains early Indian methods and techniques developed in central and western parts of the Arabic areas and in Europe. This study supports hypotheses previously formulated by Luckey and Chemla on an early scientific connection between China and Persia. 相似文献
997.
998.
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
999.
Abdelouaheb Ardjouni Ahcene Djoudi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(6):2062-2070
In this paper we consider the asymptotic stability of a generalized linear neutral differential equation with variable delays by using the fixed point theory. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton (2003) [3], Zhang (2005) [14], Raffoul (2004) [13], and Jin and Luo (2008) [12]. Two examples are also given to illustrate our results. 相似文献
1000.
R. Kasimbeyli 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2534-2547
In this paper we study optimality conditions for optimization problems described by a special class of directionally differentiable functions. The well-known necessary and sufficient optimality condition of nonsmooth convex optimization, given in the form of variational inequality, is generalized to the nonconvex case by using the notion of weak subdifferentials. The equivalent formulation of this condition in terms of weak subdifferentials and augmented normal cones is also presented. 相似文献