Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.

ANTI-PERIODIC SOLUTIONS FOR DIFFERENTIAL INCLUSIONS IN BANACH SPACES AND THEIR APPLICATIONS

We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.

Existence and Exponential Stability of the Anti-Periodic Solutions for a Class of Impulsive CohenGrossberg Neural Networks with Mixed Delays

In this paper,we study the anti-periodic solutions for a class of impulsive Cohen-Grossberg neural networks with mixed delays.By using analysis techniques,some sufficient conditions are obtained which guarantee the existence and global exponential stability of the anti-periodic solutions.The criteria extend and improve some earlier results.Moreover,we give an examples to illustrate our main results.

Existence and Uniqueness of Anti-periodic Solutions for 2n-order Differential Equations

In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.

WEIGHTED PSEUDO ALMOST-PERIODIC SOLUTIONS OF SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH MIXED DELAYS

In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays. Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper complement the previously known ones. Finally, an illustrative example is given to demonstrate the effectiveness of our results.

Anti-periodic traveling wave solution to a forced two-dimensional generalized KdV-Burgers equation

The anti-periodic traveling wave solutions to a forced two-dimensional generalized KdV-Burgers equation are studied. Some theorems concerning the boundness, existence and uniqueness of the solution to this equation are proved.

Travelling Wave Solutions of Kaup-Kupershmidt Equation Which Describes Pseudo Spherical Surfaces

In this paper I introduce the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudo-spherical surface for Kaup-Ku-pershmidt Equation with constant Gaussian curvature –1. I obtained new soliton solutions for Kaup-Kupershmidt Equation by using the modified sine-cosine method.

Existence of Anti-periodic Solution for Differential Equations

In this paper,we discuss the anti-periodic boundary value problem for a class of first order differential equations.By using homotopy method,we obtain the conditions for the existence of anti-periodic solution for the equation under consideration.This result can be extended to higher order differential equations.

NONEXISTENCE OF PSEUDO-SELF-SIMILAR SOLUTIONS TO INCOMPRESSIBLE EULER EQUATIONS

In this paper we study a generalization of self-similar solutions. We show that just as for the solutions to the Navier-Stokes equations these supposedly singular solution reduce to the zero solution.

Positive Pseudo-Symmetric Solutions for Some Nonlinear Systems at Resonance

By means of an extension of Mawhin＇s continuation theorem due to Ge,this work shows the existence of at least one positive pseudo-symmetric solution of the multi-point boundary value system.The interesting fact is that the nonlinear terms are involved in the first order derivatives.

BIFURCATION SOLUTIONS TO A BOUNDARY LAYER PROBLEM ARISING IN THE THEORY OFPOWER LAW FLUIDS

The present paper deals with a singular nonlinear boundary value problem arising in the theory of power law fluids, sufficient conditions for the existence of bifurcation solutions to the problem are obtained.

基于虚拟激励法的大跨度桥梁非平稳随机振动分析闭合解

针对大跨度结构考虑地面空间运动的非一致地震响应分析问题,结合虚拟激励法,应用傅里叶分析建立了结构非平稳随机振动响应演变功率谱分析的频域方法。建立的方法完全基于频域执行,给出了响应演变功率谱的闭合解表达式。由于实现了确定性调制过程与随机过程的有效分离,应用离散傅里叶变换进行计算不需要较高的采样分析频率就可以获得较好精度的数值结果。数值算例研究了某斜拉桥的考虑地面运动空间效应非平稳随机地震响应,与通常时频分析方法进行对比,验证了本文频域方法的正确性和有效性。

电性源瞬变电磁法虚拟波场解析推导

瞬变电磁场至虚拟波场的转换是瞬变电磁拟地震处理的基础,瞬变电磁场满足扩散方程,而虚拟波场满足波动方程,二者之间通过Q变换相互转换。将瞬变电磁数据转换成虚拟波场属于积分反变换,具有典型的不适定特性,以往主要采用数值方法求解该积分反变换。在数值求解中,需对求解方法和参数进行优化,以获得最佳求解效果。为此,本文推导了电性源瞬变电磁法电场响应的虚拟波场解析解。从均匀半空间电磁场响应的解析解出发,借助于拉普拉斯变换对,得到了阶跃响应和脉冲响应的解析表达式,从而建立起瞬变电磁场和虚拟波场的解析变换对。该解析变换对能够用于测试数值求解方法的准确性和稳定性,还能用于检验虚拟波场特性,从而形成有效的虚拟波成像方法。

基于OC&PGMF的弱监督行人检测方法

为解决弱监督行人检测训练过程中数据收敛到局部最优解和缺少回归能力问题,提出一种基于改进的在线学习与伪真值挖掘过滤算法的弱监督行人检测方法。采用WSDDN作为基础的弱监督检测器,通过优化OICR在线学习精细化策略,增加行人检测召回率并覆盖行人完整的位置,改善算法收敛到局部最优解的问题;基于邻域融合原理,通过设计伪真值挖掘过滤算法优化伪真值,进行全监督行人检测器训练,提高弱监督行人检测器的回归能力。实验结果表明,所提弱监督检测方法在VOC2007上实现了21.3%的mAP准确率,高于经典的弱监督行人检测方法(PCL)3.5%mAP准确率,验证了其有效性。

具幂次非线性项的伪抛物型方程的精确解

研究具幂次非线性项的伪抛物型方程.利用二阶微分方程作为辅助方程,对伪抛物型方程的解进行合理假设,将原方程转化为一组复杂代数方程并借助于计算机代数系统进行求解,最终获得了伪抛物型方程具有tanh函数形式、三角函数形式和有理函数形式的新精确解.

强夯加固粉土地基的竖向附加动应力传递特性

强夯法在各类地基处理项目中得到了广泛应用,但其加固机理仍落后于实践,特别是强夯引起的地基内部竖向附加动应力传递特性。鉴于此,先基于Boussinesq应力解和动量定理推导强夯竖向附加动应力和附加剪应力拟静力解。然后,以新疆维吾尔自治区乌鲁木齐市机场北区扩建项目为工程背景,运用夯锤速度法,模拟1000~4000 kN·m能级间强夯引起的动力波传播过程、竖向附加动应力传递特性和夯后土体位移场。最后,将拟静力解与动力数值解的计算结果进行对比分析。研究结果表明:强夯引起的动力波传播呈半圆弧形,竖向附加动应力传递呈半椭圆形。动力波的传播距离决定了强夯影响范围,竖向附加动应力显著区边界决定了强夯有效加固区。由拟静力解得到的竖向附加动应力相比数值解沿深度方向的衰减更快。该研究结果可为强夯法地基处理工程提供重要参考。

一类线性微分方程的指数增长型伪概反自守解

为了探讨微分系统指数增长型伪概反自守温和解的相关动力学性质。首先,将伪概自守函数的概念推广到伪概反自守函数。其次,讨论了伪概反自守函数的相关性质,证明了全体伪概反自守函数构成的集合,在无穷范数下,成为一个Banach空间。最后,利用C_(0)-半群相关理论,得到一类线性微分方程具有指数增长型的伪概反自守温和解存在并且唯一的充分条件。

EXISTENCE AND UNIQUENESS OF ANTI-PERIODIC SOLUTIONS TO AN nTH-ORDER NONLINEAR DIFFERENTIAL EQUATION WITH MULTIPLE DEVIATING ARGUMENTS

In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating arguments.

Existence of anti-periodic solutions for hemivariational inequalities

J.Y. Park and T. G. Ha [Nonlinear Anal., 2008, 68： 747-767; 2009, 7h 3203-3217] investigated the existence of anti-periodic solutions for hemivariational inequalities with a pseudomonotone operator. In this note, we point out that the methods used there are not suitable for the proof of the existence of anti-periodic solutions for hemivariational inequalities and we shall give a straightforward approach to handle these problems. The main tools in our study are the maximal monotone property of the derivative operator with anti- periodic conditions and the surjectivity result for L-pseudomonotone operators.

ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES

In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations contain nonlinear monotone operators and a nonmonotone perturbation. Moreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of secondorder nonlinear evolution equations is verified. Our abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.