Anti-periodic solution for delayed cellular neural networks with impulsive effects

In this paper, we discuss anti-periodic solution for delayed cellular neural networks with impulsive effects. By means of contraction mapping principle and Krasnoselski’s fixed point theorem, we obtain the existence of anti-periodic solution for neural networks. By establishing a new impulsive differential inequality, using Lyapunov functions and inequality techniques, some new results for exponential stability of anti-periodic solution are obtained. Meanwhile, an example and numerical simulations are given to show that impulses may change the exponentially stable behavior of anti-periodic solution.     

一类二阶积分型发展方程反周期解问题

本文中,我们研究一类带有非单调扰动算子的二阶非线性发展方程的反周期问题,证明方程中的非单调扰动算子为极大单调的,并用极大单调算子的微单调扰动理论来证明此类方程的反周期解的存在性。     

一类泛函微分方程反周期解的存在性

研究了一类含参泛函微分方程反周期解的存在性.获得了当参数在一定范围取值时反周期解的存在性结果,得到了反周期解存在的充分条件,并通过例子表明结果的可行性.主要工具为Leray-Schauder非线性抉择.     

具有时变时滞惯性四元Hopfield神经网络反周期解的动力学研究

周期性、反周期性和概周期性是时变神经网络的重要动态行为特性.本文在不将所研究的神经网络分解为实值系统的情况下,根据重合度理论中的延拓定理和不等式技巧,通过构造不同于现有平衡点稳定性研究的李雅普诺夫函数,研究了一类具有变时滞的惯性四元Hopfield神经网络的反周期解的动力学问题,给出了上述神经网络反周期解存在的一个新的判别条件.并通过构造李雅普诺夫函数论证了上述神经网络反周期解的指数稳定性.     

Anti-periodic solutions of some nonlinear evolution equations

Following a recent work of H. Okochi in the case of evolution equations generated by subdifferential operators in a real Hilbert space, we point out that many quasi-autonomous evolution equations of non monotone type associated to odd non linear operators have some anti-periodic solutions provided the forcing term is anti-periodic. This comes from the fact that the space of anti-periodic functions is transversal to the kernel of the linear part and stable under the action of odd non linear operators. The proofs of our results combine strong a priori estimates which depend very little on the non-linearities with an application of Schauder's fixed point theorem to some related dissipative equations.     

Anti-periodic solutions to nonlinear evolution equations

We deal with anti-periodic problems for nonlinear evolution equations 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.     

The heat equation in R with anti-periodic boundary condition

1Intr0ducti0nThispaPerdeaIswiththef0llowingproblerns:whereTisanypositivenumberandaisarealnumberwithIal31.In[1],A.Pazydiscussedtheproblelnasfollows:Heobtainedtheexistenceanduniqueness0fthesolutionfor(P3)intl1espaceC[0,1lundersomehypotheses0nf.(P3)isannonlinearheatequati0nwithinitialconditionandperi0dicboundaryc0nditi0n.Recentlysomeauthorshavediscussedsomedtherentialequationswithantiperi0dicboundarycondition8([2],[3]).However,theyonlystudiedtheclassicalsolutionslikewhatA.Pazydidforperiodicb…     

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.     

Anti-periodic solutions for evolution equations associated with maximal monotone mappings

In this work, we study the anti-periodic problem for a nonlinear evolution inclusion where the nonlinear part is an odd maximal monotone mapping and the forcing term is an anti-periodic mapping. Several existence results are obtained under suitable conditions. An example is presented to illustrate the results.     

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.     

2n阶微分方程反周期解的存在性与唯一性

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.     

一类具变参数的p-Laplacian中立型泛函微分方程反周期解的存在性

应用Leray Schauder 不动点定理,研究了一类具变参数的p-Laplacian中立型泛函微分方程(φp(x′(t)-c(t)x′(t-r)))′=f(x′(t))+β(t)g(x(t-τ(t)))+e(t)的反周期解问题,得到了反周期解存在的新的结果.     

Existence of anti-periodic solutions for hemivariational inequalities

J. Y. Park and T. G. Ha [Nonlinear Anal., 2008, 68: 747-767; 2009, 71: 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 antiperiodic conditions and the surjectivity result for L-pseudomonotone operators.     

Existence of weighted pseudo anti-periodic solutions to some non-autonomous differential equations

In this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti-periodicity, which generalize respectively the well-known notions of periodicity and that of anti-periodicity. Basic properties of these new functions are discussed. Furthermore, the existence of weighted pseudo anti-periodic solutions to some damped non-autonomous second-order differential equations will be investigated. To illustrate our abstract results, the existence of weighted pseudo anti-periodic solutions to a plate-like equation is discussed.     

Three anti-periodic solutions for second-order impulsive differential inclusions via nonsmooth critical point theory

A nonsmooth version of a three critical point theorem of Ricceri (due to Iannizzotto) is used to obtain three anti-periodic solutions for a second-order impulsive differential inclusions with a perturbed nonlinearity and two parameters.     

二阶微分方程反周期边值问题解的存在性

在这篇文章中,我们考虑了一类非线性二阶常微分方程反周期边值问题．利用上下解方法结合单调迭代技巧,我们得到了解的存在性结果．     

Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential

Coupled-mode systems are used in physical literature to simplify the nonlinear Maxwell and Gross–Pitaevskii equations with a small periodic potential and to approximate localized solutions called gap solitons by analytical expressions involving hyperbolic functions. We justify the use of the 1D stationary coupled-mode system for a relevant elliptic problem by employing the method of Lyapunov–Schmidt reductions in Fourier space. In particular, existence of periodic/anti-periodic and decaying solutions is proved and the error terms are controlled in suitable norms. The use of multi-dimensional stationary coupled-mode systems is justified for analysis of bifurcations of periodic/anti-periodic solutions in a small multi-dimensional periodic potential.     

The Rotation Number Approach to Eigenvalues of the One-Dimensional p-Laplacian with Periodic Potentials

The paper studies the periodic and anti-periodic eigenvaluesof the one-dimensional p-Laplacian with a periodic potential.After a rotation number function () has been introduced, itis proved that for any non-negative integer n, the endpointsof the interval ^–1(n/2) in R yield the corresponding periodicor anti-periodic eigenvalues. However, as in the Dirichlet problemof the higher dimensional p-Laplacian, it remains open if theseeigenvalues represent all periodic and anti-periodic eigenvalues.The result obtained is a partial generalization of the spectrumtheory of the one-dimensional Schrödinger operators withperiodic potentials.     

Existence of anti-periodic mild solutions for semilinear evolution equations

In this paper we study the existence of anti-periodic mild solutions for a class of semilinear evolution equations in Banach spaces and extend some related results in this direction. An example is given to illustrate our results.