Flocking and asymptotic velocity of the Cucker–Smale model with processing delay

The processing delay is incorporated into the influence function of the well-known Cucker–Smale model for self-organized systems with multiple agents. Both symmetric and non-symmetric pairwise influence functions are considered, and a Lyapunov functional approach is developed to establish the existence of flocking solutions for the proposed delayed Cucker–Smale model. An analytic formula is given to calculate the asymptotic flocking velocity in terms of model parameters and the variation of the position during the initial time interval.     

Standing waves for 4‐superlinear Schrödinger‐Kirchhoff equations

We consider standing waves for 4‐superlinear Schrödinger–Kirchhoff equations in with potential indefinite in sign. The nonlinearity considered in this study satisfies a condition that is much weaker than the classical Ambrosetti–Rabinowitz condition. We obtain a nontrivial solution and, in the case of odd nonlinearity, an unbounded sequence of solutions via the Morse theory and the fountain theorem, respectively. Copyright © 2014 John Wiley & Sons, Ltd.     

一类描述混沌映射的符号动力系统

本文定义了符号空间上的拟移位映射,并用该类映射描述了Ｃａｎｔｏｒ集及平面Ｃａｎｔｏｒ集上的混沌映射,本文结果可看作Ｓｍａｌｅ马蹄模型的简化。     

Existence of multiple nontrivial solutions for a Schrödinger–Poisson system

We consider a Schrödinger–Poisson system in R³${\mathbb{R}}^3$ with potential indefinite in sign and a general nonlinearity. We use the direct variational method and Morse theory to obtain the existence of multiple nontrivial solutions for this system.     

Chaos in a mapping describing elastoplastic oscillations

We study the local and global dynamical behavior of a two dimensional piecewise linear map which describes the asymptotic motions of a single degree of freedom, parametrically excited, elastoplastic oscillator after it has settled down to purely elastic oscillations. We give existence and stability conditions for periodic orbits and prove that chaos, in the form of a Smale horseshoe, exists at specific, but representative, parameter values. We interpret simulations of the elastoplastic oscillator itself in the light of these results.Partially supported by NSF grant number MSS-9016626.Partially supported by AFOSR 91-0329.     

Genericity of Well-Posedness, Perturbations and Smooth Variational Principles

We show that three important topics in nonlinear analysis and optimization are intimately related: the theory of perturbations, the notion of well-posedness and variational principles in the sense of Ekeland, Borwein–Preiss and Deville–Godefroy–Zizler. The concept of genericity and the new notion of flexible perturbation play a key role in these connections. This notion enables one to consider topologies on spaces of functions which have been introduced recently. A link between the Asplund and Ekeland–Lebourg methods and the Palais–Smale condition, another important topic in nonlinear analysis, is pointed out.     

SMALE HORSESHOES AND CHAOS IN DISCRETIZED PERTURBED NLS SYSTEMS(Ⅰ)-POINCAR(E) MAP

The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger(NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invariant set Λ on which the dynamics is topologically conjugate to a shift on four symbols.     

SMALE HORSESHOES AND CHAOS IN DISCRETIZED PERTURBED NLS SYSTEMS(Ⅱ)—SMALE HORSESHOES

2000MathematicsSubjectClassification:35Q Introduction ContinueRef.[1],inthispart,weapplythegeneralizedConley Moserconditions[2]toshowtheexistenceofSmalehorseshoesinbelowthediscreteNLSsystems(1).Considerthefollowingn particle(any2相似文献   

具Hardy-Sobolev临界指数椭圆方程的非平凡解

运用精确估计和变分法得到具奇异位势的椭圆方程-△u-μu/|x|2=|u|2*(s)-2u/|x|s+λu,u∈H0(1,2)(Ω)的非平凡解的存在性,其中Ω是有光滑边界的有界开区域,μ,λ是两个正参数.