Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional <i>q</i>-Difference Equation

In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions are obtained.

Existence of Multiple Positive Solutions of Discrete Boundary Value Problem

In this paper, we consider the existence of multiple positive solutions of discrete boundary value problem. The theory of fixed point index is used here to derive the existence theorem.

具有无界势能的Kirchhoff-型差分方程多个同宿轨的存在性

该文运用临界点理论研究了具有无界势能的Kirchhoff-型差分方程多个同宿轨的存在性.特别地,文中借助于非线性项次线性增长条件和一些技巧证明了能量泛函满足Palais-Smale紧性条件.最后举例说明主要结论.

Existence of Three Positive Periodic Solutions of Neutral Nonlinear Functional Difference Equations

This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.

Existence and Multiple of Positive Solution for Nonlinear Fractional Difference Equations with Parameter

Let,. We study the existence and multiple positive solutions of n-th nonlinear discrete fractional boundary value problem of the form By using a fixed-point theorem on cone, the parameter intervals of problem is established.

ANALYTIC SOLUTIONS OF SYSTEMS OF FUNCTIONAL EQUATIONS

Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. For any subset K of C and any integer m≥1, write A(D m,K)={f|f∶D m→K is a continuous map, and f|(D m)° is analytic}. For H∈ A(D m,C)(m≥2), f∈A(D,D) and z∈D, write Ψ H(f)(z)=H(z,f(z),...,f m-1(z)). Suppose F,G∈A(D 2n+1,C), and H k,K k∈A(D k,C), k=2,...,n. In this paper, the system of functional equations F(z,f(z),f 2(Ψ H 2(f)(z)),...,f n(Ψ H n(f)(z)),g(z),g 2(Ψ K 2(g)(z)),..., g n(Ψ K n(g)(z)))=0 G(z,f(z),f 2(Ψ H 2(f)(z)),...,f n(Ψ H n(f)(z)),g(z),g 2(Ψ K 2(g)(z)),..., g n(Ψ K n(g)(z)))=0(z∈D) is studied and some conditions for the system of equations to have a solution or a unique solution in A(D,D)×A(D,D) are given.

EXISTENCE OF HOMOCLINIC ORBITS FOR A CLASS OF FIRST-ORDER DIFFERENTIAL DIFFERENCE EQUATIONS

In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation z（t）＋B（t）z（t）＋f（t,z（t＋τ）,z（t）,z（t-τ））=0.

Multiple Periodic Solutions for a Class of Fourth-order Difference Systems

By using critical point theory,we study periodic solutions for a class of fourthorder difference systems with partially periodic potential and linear nonlinearity.Some sufficient conditions for the existence of multiplicity of periodic solutions are obtained via generalized saddle point theorem.

Positive periodic solutions of higher-dimensional nonlinear functional difference equations

In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the form:x(n+ 1) =A(n)x(n) +λh(n)f(x(n- τ(n))), n∈ Z.

Existence and Uniqueness of Analytic Solutions of Systems of Iterative Functional Equations

Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. Write A(D,D)={f: f is a continuous map from D into itself, and f|D ° is analytic}. Suppose G,H: D 2n+1 →C are continuous maps (n≥2), and G|(D 2n+1 ) °, H|(D 2n+1 ) ° are analytic. In this paper, we study the system of iterative functional equationsG(z,f(z),…,f n(z), g(z),…,g n(z))=0, H(z,f(z),…,f n(z), g(z),…,g n(z))=0, for any z∈D,and give some conditions for the system of equations to have a solution or a unique solution in A(D,D) ×A(D,D).

Discrete Arzelà-Ascoli Theorem on the Half Line and Its Application

The compactness criterion in l◇={x（·）∈l^∞（0,∞））｜lim t→∞ x（t）=x（∞）} is given and as an application,we study the existence of positive solutions of second order boundary value problems of difference equation on the half line by the fixedpoint theorem in cones.

THE EXISTENCE OF POSITIVE SOLUTIONS OF THE NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS IN A BANACH SPACE

In this paper, the author obtains the existence of positive solutions of nonlinear neutral differential difference equations in a Banach space by means of the fixed point theorems.

THE EXISTENCE OF MULTIPLE POSITIVE SOLUTION OF NONLINEAR NEUTRAL DIFFERENCE EQUATION

In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of nonlinear neutral difference equation.The result is illustrated by an example.

THE EXISTENCE OF MULTIPLE POSITIVE SOLUTION OF NON-AUTONOMOUS NONLINEAR NEUTRAL DIFFERENCE EQUATION

In this paper, by using the fixed point index theory, we obtain an existence criteria for multiple positive solution of non-autonomous nonlinear neutral difference equation. We extend the results in [1].

THE EXISTENCE OF PERIODIC SOLUTIONS TO SECOND ORDER SELF-ADJOINT DIFFERENCE EQUATIONS

In this paper, we consider the existence of periodic solutions to a class of second order self-adjoint difference equations. By the least action principle and saddle point theorem in the critical point theory, some new results are obtained. As an application, we also give two examples to demonstrate our main results.

基于多数据源的采煤沉陷区早期识别及地面形变特征监测——以神木市大柳塔镇为例

煤矿区生态环境问题受到社会的广泛关注,如何实现采煤沉陷区精准、高效、经济的早期识别和动态监测显得尤为迫切。本文在资料收集与整理分析的基础上,利用2000—2022年5期DEM数据进行差分解算,同时利用2015年6月15日至2023年7月15日共计164期长时间序列Sentinel-1数据,对煤矿区地面沉降进行动态监测,查明了神木市大柳塔镇采煤沉陷区现状分布与地面沉降特征,形成了一套基于多数据源的采煤沉陷区早期识别方法。研究结果表明:①大柳塔镇采煤沉陷区分布面积为252.70 km 2,包括地面塌陷、采空区悬顶两种类型,神华公司石圪台、哈拉沟、大柳塔、活鸡兔4大矿区煤矿塌陷问题严重;②将分辨率为2 m的DEM数据重采样为5 m后进行差值运算,误差为0.01 m,精度较高且计算高效;③DEM差分解算、SBAS-InSAR技术均能对地面塌陷范围进行精准识别,匹配度高,且各方法间互为补充,相互印证。

两种不同实验室对一节电工学实验的影响

以轮机工程专业的学生为授课对象,以三相鼠笼式电动机的点动自锁实验为内容,可通过在两种配有不同设备的实验室来进行实施同一节电工学实验,以比对取得的最佳实验效果。配有不同实验设备的两个实验室都能对学生学习新知识、动手能力的提高有较好的教学效果,提高学生能力最大的是在含有分离设备的实验室进行的。同一节“电工学实验”课最好的教学效果是同一个实验先后在布置有实验台的实验室和布置有分离设备的实验室顺次安排进行。

Existence of periodic and subharmonic solutions for second-order superlinear difference equations

By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_{n - 1} + f(n, x_n ) = 0,$$ some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.

Periodic solutions of a 2nth-order nonlinear difference equation

In this paper, a 2 nth-order nonlinear difference equation is considered.Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of periodic solutions.Results obtained complement or improve the existing ones.

基于LC-OPA的空间激光通信技术进展

液晶相控阵既可以在空间激光通信技术建立多点间空间激光通信链路,又能代替压电偏摆镜的精瞄方式。阐述液晶相控阵应用趋势;通过对液晶相控阵中液晶分子电致双折射和多缝衍射光束偏转原理,提出替压电偏摆镜配合终端进行瞄准捕获跟踪的方案;以“一对二”空间激光通信终端为例,提出基于液晶相控阵多点间空间激光通信终端方案和链路工作模式,分析方案优势,并进行未来展望。