Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order

In this paper, we prove the existence and uniqueness of solutions for an anti-periodic boundary value problem of nonlinear impulsive differential equations of fractional order α∈(2,3] by applying some well-known fixed point theorems. Some examples are presented to illustrate the main results.     

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．     

Anti-periodic fractional boundary value problems for nonlinear differential equations of fractional order

In this paper, the existence of solutions of an anti-periodic fractional boundary value problem for nonlinear fractional differential equations is investigated. The contraction mapping principle and Leray-Schauder’s fixed point theorem are applied to establish the results.     

Impulsive anti-periodic boundary value problem of first-order integro-differential equations

This paper is concerned with the anti-periodic boundary value problem of first-order nonlinear impulsive integro-differential equations. We first establish a new comparison principle, and then obtain the existence of extremal solutions by upper-lower solution and monotone iterative techniques. Some examples are presented to illustrate the main results.     

Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions

This paper describes the method of quasilinearization for first-order nonlinear impulsive functional differential equations with anti-periodic boundary conditions. A monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand.     

Existence of solutions for anti-periodic boundary value problems of nonlinear impulsive functional integro-differential equations of mixed type

We discuss the existence of minimal and maximal solutions for a class of first order nonlinear impulsive functional integro-differential equations of mixed type with anti-periodic boundary conditions. The main tool of study is the monotone iterative technique.     

A Coupled System of Caputo-Type Sequential Fractional Differential Equations with Coupled (Periodic/Anti-periodic Type) Boundary Conditions

In this paper, we introduce the concept of coupled (periodic/anti-periodic type) boundary conditions and solve a coupled system of nonlinear sequential fractional differential equations equipped with these conditions. Sufficient criteria ensuring the existence and uniqueness of solutions for the given problem are presented. Our results are new in the given configuration and are well illustrated with the aid of examples.     

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.     

ANTI-PERIODIC BOUNDARY VALUE PROBLEM FOR FUNCTIONAL DIFFENERTIAL EQUATION

By using upper and lower solutions coupled with monotone iterative technique, we discuss the anti-periodic boundary value problem for first order functional diffenertial equation. A sufficient condition for the existence of the solution is obtained.     

Lyapunov-type inequalities for a class of higher-order linear differential equations with anti-periodic boundary conditions

In this paper, we obtain some new Lyapunov-type inequalities for a class of higher-order linear differential equations with anti-periodic boundary value condition, the results of this paper are new and generalize and improve some early results in the literature.     

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.     

ANTI-PERIODIC BOUNDARY VALUE PROBLEM FOR FIRST ORDER DELAY DIFFERENTIAL EQUATIONS

The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results on the existence and uniqueness of the solution for anti-periodic boundary value problem of delay differential equations.     

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。     

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 for Rayleigh-type equations via the reproducing kernel Hilbert space method

In this paper, reproducing kernel theorem is employed to solve anti-periodic solutions for Rayleigh-type equations. A simple algorithm is given to obtain the approximate solutions of the equations. By comparing the approximate solution with the exact analytical solution, we find that the simple algorithm is of good accuracy and it can be also applied to some ordinary or partial differential equations with initial-boundary value conditions and nonlocal boundary value conditions.     

Existence of solutions for anti-periodic boundary value problems

By using Schauder’s fixed point theorem and the lower and upper solutions method, we discuss the anti-periodic boundary value problem for a class of second-order differential equations. Some sufficient conditions for the existence of solutions are obtained.     

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.     

多时滞抛物型微分方程的强迫振动

我们给出满足某种边界条件的非线性时滞抛物型微分方程的一切解振动的若干充分条件.     

On the Floquet problem for second-order Marchaud differential systems

Solutions in a given set of the Floquet boundary value problem are investigated for second-order Marchaud systems. The methods used involve a fixed point index technique developed by ourselves earlier with a bound sets approach. Since the related bounding (Liapunov-like) functions are strictly localized on the boundaries of parameter sets of candidate solutions, some trajectories are allowed to escape from these sets. The main existence and localization theorem is illustrated by two examples for periodic and anti-periodic problems.     

Anti-periodic solutions of higher order nonlinear difference equations: a variational approach

A 2nth order nonlinear difference equation is studied. By using a variational approach, existence results for anti-periodic solutions are obtained under various assumptions upon the nonlinearities.