Existence and continuation of periodic solutions of autonomous Newtonian systems

In this article, we study the existence and the continuation of periodic solutions of autonomous Newtonian systems. To prove the results we apply the infinite-dimensional version of the degree for SO(2)-equivariant gradient operators defined by the third author in Nonlinear Anal. Theory Methods Appl. 23(1) (1994) 83-102 and developed in Topol. Meth. Nonlinear Anal. 9(2) (1997) 383-417. Using the results due to Rabier [Symmetries, Topological degree and a Theorem of Z.Q. Wang, J. Math. 24(3) (1994) 1087-1115] and Wang [Symmetries and calculation of the degree, Chinese Ann. Math. 10 (1989) 520-536] we show that the Leray-Schauder degree is not applicable in the proofs of our theorems, because it vanishes.     

A Mathematical Programming Incremental Formulation for Unilateral Frictional Contact Problems of Linear Elasticity

In this article a detailed analytical formulation of the unilateral contact boundary conditions with Coulomb's law of dry friction is first attempted and the quasi-static contact problem between 3-D elastic bodies is studied thereafter. Discretizing the bodies by the Finite Element Method, introducing fictitious contact bonds and using the concept of the equivalent structural system, an incremental Nonlinear Complementarity Problem is finally formulated. Then, using additional simplifying assumptions, this problem can be transformed into an incremental Linear Complementarity Problem.     

基于样条变换的PLS回归的非线性结构分析

基于样条变换的:PLS非线性回归模型既吸取了样条函数分段拟合以适应任意曲线连续变化的优点,又借鉴了偏最小二乘回归方法能够有效解决自变量集合高度相关的技术.针对多元加法模型,从理论和仿真试验的角度分别验证了,对于多个独立自变量对单因变量为非线性关系的数据系统,基于样条变换的PLS回归方法不仅能够有效实现自变量对因变量的整体预测,而且能够提取各维自变量对因变量的单独非线性作用特征,从而确定数据系统内部的复杂非线性结构关系,增强了模型的可解释性.     

Identification of Piecewise-Constant Potentials by Fixed-Energy Phase Shifts

The identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely defined by a sufficiently large subset of its phase shifts at any one fixed energy level. However, two different potentials can produce almost identical phase shifts. To resolve this difficulty we suggest the use of phase shifts corresponding to several energy levels. The identification is done by a nonlinear minimization of the appropriate objective function. It is based on a combination of probabilistic global and deterministic local minimization methods. The Multilevel Single-Linkage Method (MSLM) is used for the global minimization. A specially designed Local Minimization Method (LMM) with a Reduction Procedure is used for the local searches. Numerical results show the effectiveness of this procedure for potentials composed of a small number of spherical layers. Accepted 2 February 2001. Online publication 11 May 2001.     

Numerical and theoretical study of a Dual Mesh Method using finite volume schemes for two phase flow problems in porous media

Summary. In this paper we are interested in two phase flow problems in porous media. We use a Dual Mesh Method to discretize this problem with finite volume schemes. In a simplified case (elliptic - hyperbolic system) we prove the convergence of approximate solutions to the exact solutions. We use the Dual Mesh Method in physically complex problems (heterogeneous cases with non constant total mobility). We validate numerically the Dual Mesh Method on practical examples by computing error estimates for different test-cases. Received March 21, 1997 / Revised version received October 13, 1997     

Nonlinear analysis and complementarity theory

We present in this paper a short survey of some recent interactions between Nonlinear Analysis and Nonlinear Complementarity. Considering the new relations between Nonlinear Analysis and Complementarity Theory, put in evidence in this paper, we define several open research subjects profitable to both domains.     

Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions

Summary. Multilevel Schwarz methods are developed for a conforming finite element approximation of second order elliptic problems. We focus on problems in three dimensions with possibly large jumps in the coefficients across the interface separating the subregions. We establish a condition number estimate for the iterative operator, which is independent of the coefficients, and grows at most as the square of the number of levels. We also characterize a class of distributions of the coefficients, called quasi-monotone, for which the weighted -projection is stable and for which we can use the standard piecewise linear functions as a coarse space. In this case, we obtain optimal methods, i.e. bounds which are independent of the number of levels and subregions. We also design and analyze multilevel methods with new coarse spaces given by simple explicit formulas. We consider nonuniform meshes and conclude by an analysis of multilevel iterative substructuring methods. Received April 6, 1994 / Revised version received December 7, 1994     

Stationary Distribution and Extinction of a Stochastic HIV-1 Infection Model with Distributed Delay and Logistic Growth

Journal of Nonlinear Science - In this paper, we propose a stochastic HIV-1 infection model with distributed delay and logistic growth. Firstly, we transfer the stochastic model with weak kernel...     

LOCALLY STABILIZED FINITE ELEMENT METHOD FOR STOKES PROBLEM WITH NONLINEAR SLIP BOUNDARY CONDITIONS

Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.     

Long-Time Asymptotics for Homoenergetic Solutions of the Boltzmann Equation: Collision-Dominated Case

Journal of Nonlinear Science - In this paper, we present a formal analysis of the long-time asymptotics of a particular class of solutions of the Boltzmann equation, known as homoenergetic...     

Variational Evolution of Dislocations in Single Crystals

Journal of Nonlinear Science - In this paper, we provide an existence result for the energetic evolution of a set of dislocation lines in a three-dimensional single crystal. The variational problem...     

Adaptive Dynamics of a Stoichiometric Phosphorus–Algae–Zooplankton Model with Environmental Fluctuations

Journal of Nonlinear Science - In this paper, we introduce a theoretical framework for semi-discrete optimization using ideas from optimal transport. Our primary motivation is in the field of deep...     

A comment on the papers: Controllability results for functional semilinear differential inclusions in Fréchet spaces [Nonlinear Anal. 61 (3) (2005) 405–423] and Controllability of impulsive neutral functional differential inclusions with infinite delay [Nonlinear Anal. 60 (8) (2005) 1533–1552]

In this note we make some observations relating two papers recently published in Nonlinear Analysis Theory, Methods & Applications.     

Boltzmann and Fokker–Planck Equations Modelling the Elo Rating System with Learning Effects

Journal of Nonlinear Science - In this paper, we propose and study a new kinetic rating model for a large number of players, which is motivated by the well-known Elo rating system. Each player is...     

Linear maps on the space of all bounded observables preserving maximal deviation

In this paper we determine all the bijective linear maps on the space of bounded observables which preserve a fixed moment or the variance. Nonlinear versions of the corresponding results are also presented.     

Asymmetric positive solutions for a symmetric nonlinear problem in {\mathbb R}^N

We study a symmetric semilinear elliptic problem in all and we prove existence of an asymmetric positive solution by using variational arguments. The corresponding problem in dimension N=2, which provides the motivation of this work, arises in Nonlinear Optics from the study of the behaviour of optical cylindrical waveguides. Received September 28, 1999/ Accepted January 14, 2000 / Published online June 28, 2000     

Multiple Solutions for Gradient Elliptic Systems with Nonsmooth Boundary Conditions

In this paper we prove the existence of at least three solutions of gradient elliptic systems with nonhomogeneous and nonsmooth Neumann boundary conditions. Our investigations complete the results of J. Fernandez Bonder, S. Martinez, J.D. Rossi (NoDEA Nonlinear Differential Equations Appl. 2007). We use a recent generalization of a three critical points theorem of B. Ricceri (Nonlinear Anal. 2008) for locally Lipschitz functionals given by A. Kristály, W. Marzantowicz, Cs. Varga (J. Global Optim. 2010).     

本刊英文版Vol.31(2015),No.6论文摘要（英文）

<正>Multiple Positive Solutions for a Nonlinear Elliptic Equation Involving Hardy-Sobolev-Maz'ya Term Shuang Jie PENG Jing YANG Abstract In this paper,we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy-Sobolev-Maz'ya term:     

Dynamics of Nonlinear Random Walks on Complex Networks

Journal of Nonlinear Science - In this paper, we study the dynamics of nonlinear random walks. While typical random walks on networks consist of standard Markov chains whose static transition...     

Modified Lagrangian and Least Root Approaches for General Nonlinear Optimization Problems

Abstract In this paper we study nonlinear Lagrangian methods for optimization problems with side constraints.Nonlinear Lagrangian dual problems are introduced and their relations with the original problem are established.Moreover,a least root approach is investigated for these optimization problems.