We consider a kind of Liénard equations with deviating argument. Using the fixed-point theorem in cone and analytical technique, we obtain the existence of positive periodic solution to the problem under the appropriate conditions. Some examples are presented to illustrate our results.

We prove a version of the Picard-Schottky theorem involving the multiplicity for quasiregular in n-dimensional Euclidean space Rn. We also study the boundary behavior of quasiregular mappings from the unit ball Bn into a multiply punctured space Rn∖{w1,…,wp−1}.

In this paper, we study the existence, nonexistence, and multiplicity of positive solutions to a nonlinear impulsive Sturm–Liouville boundary value problem with a parameter. By using a variational method, we prove that the problem has at least two positive solutions for the parameter λ∈ (0,Λ ) , one positive solution for λ =Λ , and no positive solution for λ >Λ , where Λ >0 is a constant.

We introduce a new method for the Monte Carlo simulation of a weak solution of the Schrödinger-type equation where the potential is piecewise constant and positive. The method, called the killing walk-on-spheres algorithm, combines the classical walk-on-spheres algorithm with killing that can be determined by using panharmonic measures. This paper continues our earlier work in which simulation of the solutions of the Yukawa and the Helmholtz partial differential equations were developed.

在核心素养视角下,当前小学数学课堂教学中人文素养培养的研究主要以提出实施办法为主,国际组织和各国(地区)都建立了结构完整的核心素养体系,并将其纳入学科培养目标.打破传统教学方式,开展以生为本的多样化教学;把握数学人文力量,文理结合促发展;加强沟通,注重课堂评价,播撒人文关怀是人文素养培养在小学数学课堂教学中融入的有效途径.

本文通过调查研究和数据分析,运用问卷调查法、对比实验法、典型调查法,基于SEM模型和层次分析法,有效地配备垃圾桶.通过方案的确定与选择,最终确定了最佳方案:在家中增设2个垃圾桶,楼道垃圾桶离楼梯口的距离应在3～10米,且应该将不同种类的分类垃圾桶摆放在同一个地点,便于住户在出门时可同时完成扔垃圾和处理垃圾,从而激励人们对于垃圾分类行为的主动性,有助于分类意识的养成,从而合理有效地回收生活垃圾,保护自然资源和生态环境.

We show that a constant-potential time-independent Schrödinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the Duffin correspondence, we provide a classical Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the boundary value problem. We compare the obtained Duffin WOS algorithm with existing modified WOS algorithms.

和国际小学数学课程标准对比,我们需要在小学数学课程标准中构建“数学素养”的教学框架、提升小学数学教师素质、加强以育人为本的精细化小学数学教学设计,以推进我国小学数学课堂的素养教学.在具体实施素养教学中,数学教师要创造性地将各门学科知识内容与数学教学内容相联系、在教学过程中结合具体教学内容增强学生的数学探究体验以及要注重在社会生活中应用数学的引领,促进小学数学教师在实际课堂教学中落实素养教学.

In this paper, we investigate the modified function projective lag synchronization for two different stochastic chaotic systems using adaptive control method. We design an adaptive controller to make the mean square of synchronization error convergence to an arbitrarily small bound around zero depending on the controller feedback gain according to the Lyapunov stability theory. One example is presented to demonstrate the effectiveness of the proposed controller.

本文基于经典的阶段结构模型和Lotka-Volterra捕食模型,提出和研究了具有比率依赖型功能性反应模式的脉冲非自治两维时滞微分方程的周期性释放天敌在固定时刻对害虫控制的过程.得到了害虫灭绝周期解的全局吸引性和依赖于时滞和脉冲的人口模型持久性的条件.

In this paper, we investigate the existence of infinite nonradial solutions for the Schrodinger equations ( 4 u + b(jxj)u = f(jxj, u), x2 R N , u2 H 1 (R N ),

In this paper, we study the existence of nontrivial solutions for the second-order three-point boundary value problem with impulses. Under certain growth conditions on the nonlinearity function and by using Leray-Schauder nonlinear alternative, sufficient conditions for the existence of a nontrivial solution are obtained. Furthermore, we illustrate our results with some examples.

The existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using a fixed point theorem in cone, we obtain two existence results, which extend some known results.

We study the existence of periodic solutions for third-order nonlinear differential equations. The method of proof relies on Schauder's fixed point theorem applied in a novel way, where the original equation is transformed into second-order integrodifferential equation through a linear integral operator. Finally, examples are presented to illustrate applications of the main results.

In this paper, an adaptive fuzzy controller is designed for a nonlinear stochastic system to track the given reference via the sliding mode method. The nonlinear stochastic system is modeled by a deterministic nonlinear system with white noise obtained from the derivative of a Wiener process, which eventually generates an Itô differential equation. Compared with existing results, the main advantage is that information of the nonlinear functions is not required. Under the designed controller with the proposed update laws, the tracking error trajectories converge to an arbitrary small region around zero in the mean square norm. Simulations to show the efficiency of the proposed controller are provided.

We study solvability of nonlocal boundary value problems for second-order differential equations with resonance or non-resonance. The method of proof relies on Schauder’s fixed point theorem. Some examples are presented to illustrate the main results.

This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu) in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller.

We consider a multi-point boundary value problem for second-order impulsive differential equations. By using a fixed-point theorem due to Avery and Peterson [1], we obtain the sufficient conditions for the existence of at least three positive solutions. An example is worked out to demonstrate the main result.

We consider the existence of multiple positive solutions of the Singular Boundary Value Problem for Sturm-Liouville equations with impulses. By using a fixed-point index theorem of cone map, some existence and multiplicity results positive solutions are obtained. Our results improve and generalise those in some well-known results. Some examples are presented to demonstrate the application of our main results.

We study the existence of solutions to the Duffing equation with impulses. By means of the Poincare-Birkhoff fixed point theorem under given conditions, we obtain the sufficient condition of existence of infinitely many solutions. Our results generalize those of T. R. Ding. An example is presented to demonstrate applications of our main result.