“一类二阶中立型泛函微分方程的振动性”的注记

给出了标题中所述文章的一个注记.指出前提条件之一不成立,从而其所有定理均不成立.     

A new method for a class of linear variational inequalities

In this paper we introduce a new iterative scheme for the numerical solution of a class of linear variational inequalities. Each iteration of the method consists essentially only of a projection to a closed convex set and two matrix-vector multiplications. Both the method and the convergence proof are very simple.This work is supported by the National Natural Science Foundation of the P.R. China and NSF of Jiangsu.     

Convexity estimates for nonlinear elliptic equations and application to free boundary problems

We prove the convexity of the set which is delimited by the free boundary corresponding to a quasi-linear elliptic equation in a 2-dimensional convex domain. The method relies on the study of the curvature of the level lines at the points which realize the maximum of the normal derivative at a given level, for analytic solutions of fully nonlinear elliptic equations. The method also provides an estimate of the gradient in terms of the minimum of the (signed) curvature of the boundary of the domain, which is not necessarily assumed to be convex.     

Nonlinear Sigma Models in (1+2) Dimensions and an Infinite Number of Conserved Currents

In this Letter, we treat nonlinear sigma models such as the C P¹-model, Q P¹-model, etc. in 1+2 dimensions. For submodels of such models, we definitely construct an infinite number of nontrivial conserved currents. Our result is a generalization of Alvarez, Ferreira and Guillen.     

Design and optimal tuning of nonlinear PI compensators

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by linear proportional and integral (PI) compensators are considered. For such systems, a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution.Additionally, a general nonlinear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear PI compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over linear PI compensators is discussed and is demonstrated for two feedback systems.     

Vector complementarity problems with a variable ordering relation

In this paper, we investigate vector complementarity problems with a variable ordering relation. We establish existence results of a solution of a vector complementarity problem under an inclusive type condition. We obtain equivalence results among a vector complementarity problem, a vector variational inequality problem and other related problems.     

一类非线性双曲方程整体弱解的存在性及能量衰减性

讨论了一类非线性双曲方程u_u-m(‖▽u‖_2~2)△u-γ△u_t=β|u|~αu的初边值问题整体弱解的存在性和指数衰减..     

Half-line solutions of a nonlinear heat conduction problem

We solve a half-line problem for a nonlinear diffusion equation with a given time-dependent thermal conductivity at the origin. The problem reduces to a linear Volterra integral equation, which is solvable by Picard’s process of successive approximations. We analyze some explicit examples numerically. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 58–65, July, 2007.     

A New General Algebraic Method and Its Application to Shallow Long Wave Approximate Equations

A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.     

Applications of Elliptic Equation to Nonlinear Coupled Systems

The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. Itis shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wavesolutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.