Discrete & Continuous Dynamical Systems - S最新文献

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Infinitely many positive solutions for Schrödinger-poisson systems with nonsymmetry potentials 具有非对称势的Schrödinger-poisson系统的无穷多正解

Discrete & Continuous Dynamical Systems - S

Pub Date : 2021-01-01 DOI: 10.3934/DCDS.2021054

Fang Qin, Jun Wang, Jing Yang

The present paper deals with a class of Schrodinger-poisson system. Under some suitable assumptions on the decay rate of the coefficients, we derive the existence of infinitely many positive solutions to the problem by using purely variational methods. Comparing to the previous works, we encounter some new challenges because of nonlocal term. By doing some delicate estimates for the nonlocal term we overcome the difficulty and find infinitely many positive solutions.

本文讨论了一类薛定谔-泊松系统。在有关系数衰减率的适当假设下，用纯变分方法导出了该问题的无穷多个正解的存在性。与以往的工作相比，由于非本地术语的存在，我们遇到了一些新的挑战。通过对非局部项做一些精细的估计，我们克服了这个困难，找到了无穷多个正解。

引用次数: 2

State feedback for set stabilization of Markovian jump Boolean control networks 马尔可夫跳变布尔控制网络集镇定的状态反馈

Discrete & Continuous Dynamical Systems - S

Pub Date : 2021-01-01 DOI: 10.3934/dcdss.2020413

Sanmei Zhu, Jun‐e Feng, Jianli Zhao

In this paper, the set stabilization problem of Markovian jump Boolean control networks (MJBCNs) is investigated via semi-tensor product of matrices. First, the conception of set stabilization is proposed for MJBCNs. Then based on the algebraic expression of MJBCN, a necessary and sufficient condition for set stabilization is provided by a linear programming problem, which is simple to solve. Moreover, by solving this linear programming problem, an algorithm for designing a state feedback controller is developed. Finally, two examples are presented to illustrate the feasibility of the obtained results.

本文利用矩阵的半张量积研究了马尔可夫跳布尔控制网络的集镇定问题。首先，提出了mjbcn的集镇定概念。然后根据MJBCN的代数表达式，通过求解一个简单的线性规划问题，给出了集合稳定的充分必要条件。此外，通过求解该线性规划问题，提出了一种状态反馈控制器的设计算法。最后，通过两个算例说明所得结果的可行性。

引用次数: 3

Erratum and addendum to "A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies" (Volume 40, Number 4, 2020, 2285-2313) “远离切线的非奇异自同态的一个正向遍历闭合引理和熵猜想”的勘误和增补(卷40，第4期，2020,2285-2313)

Discrete & Continuous Dynamical Systems - S

Pub Date : 2021-01-01 DOI: 10.3934/dcds.2021196

S. Hayashi

We add a lemma implicitly used in the proof of the forward Ergodic Closing Lemma in the paper "A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies" [Discrete Contin. Dyn. Syst., 40 (2020), 2285-2313].

在“远离切线的非奇异自同态的正遍历闭引理与熵猜想”[离散连续]一文中，我们增加了证明正遍历闭引理中隐式使用的一个引理。直流发电机系统。生态学报，40(2020)，2285-2313。

引用次数: 0

Galerkin method of weakly damped cubic nonlinear Schrödinger with Dirac impurity, and artificial boundary condition in a half-line 含Dirac杂质的弱阻尼三次非线性Schrödinger的Galerkin方法，以及半线上的人工边界条件

Discrete & Continuous Dynamical Systems - S

Pub Date : 2021-01-01 DOI: 10.3934/DCDSS.2021030

A. Chrifi, M. Abounouh, H. A. Moatassime

We consider a weakly damped cubic nonlinear Schrodinger equation with Dirac interaction defect in a half line of begin{document}$ mathbb{R} $end{document} . Endowed with artificial boundary condition at the point begin{document}$ x = 0 $end{document} , we discuss the global existence and uniqueness of solution of this equation by using Faedo–Galerkin method.

引用次数: 2

On the number of limit cycles of a quartic polynomial system 关于一个四次多项式系统的极限环的个数

Discrete & Continuous Dynamical Systems - S

Pub Date : 2021-01-01 DOI: 10.3934/dcdss.2020337

Min Li, Maoan Han

In this paper, we consider a quartic polynomial differential system with multiple parameters, and obtain the existence and number of limit cycles with the help of the Melnikov function under perturbation of polynomials of degree begin{document}$ n = 4 $end{document}.

引用次数: 0

Some new bounds analogous to generalized proportional fractional integral operator with respect to another function 关于另一个函数的一些类似于广义比例分数积分算子的新界

Discrete & Continuous Dynamical Systems - S

Pub Date : 2021-01-01 DOI: 10.3934/DCDSS.2021020

S. Rashid, F. Jarad, Z. Hammouch

The present article deals with the new estimates in the view of generalized proportional fractional integral with respect to another function. In the present investigation, we focus on driving certain new classes of integral inequalities utilizing a family of positive functions begin{document}$ n(ninmathbb{N}) $end{document} for this newly defined operator. From the computed outcomes, we concluded some new variants for classical generalized proportional fractional and other integrals as remarks. These variants are connected with some existing results in the literature. Certain interesting consequent results of the main theorems are also pointed out.

引用次数: 11

High and low perturbations of Choquard equations with critical reaction and variable growth 具有临界反应和变增长的Choquard方程的高低摄动

Discrete & Continuous Dynamical Systems - S

Pub Date : 2021-01-01 DOI: 10.3934/dcds.2021180

Youpei Zhang, Xianhua Tang, V. Rǎdulescu

We are concerned with the existence of ground state solutions to the nonhomogeneous perturbed Choquard equation

begin{document}$ - Delta_{p(x)} u + V(x)|u|^{p(x) - 2} u $end{document}

begin{document}$ = left( int_{mathbb R^N} r(y)^{-1}|u(y)|^{r(y)}|x-y|^{-lambda(x,y)} dyright) |u|^{r(x)-2} u+g(x,u) mbox{in} mathbb R^N, $end{document}

where the exponent begin{document}$ r(cdot) $end{document} is critical with respect to the Hardy-Littlewood-Sobolev inequality for variable exponents. We first consider the case where the perturbation begin{document}$ g(cdot ,cdot) $end{document} is subcritical and we distinguish between the superlinear and sublinear cases. In both situations we establish the existence of solutions and we prove the asymptotic behavior of low-energy solutions in the case of high perturbations. Next, we study the case where the nonlinearity begin{document}$ g(cdot ,cdot) $end{document} is critical. We prove the existence of solutions both for low and high perturbations and we establish asymptotic properties of low-energy solutions.

We are concerned with the existence of ground state solutions to the nonhomogeneous perturbed Choquard equation begin{document}$ - Delta_{p(x)} u + V(x)|u|^{p(x) - 2} u $end{document} begin{document}$ = left( int_{mathbb R^N} r(y)^{-1}|u(y)|^{r(y)}|x-y|^{-lambda(x,y)} dyright) |u|^{r(x)-2} u+g(x,u) mbox{in} mathbb R^N, $end{document} where the exponent begin{document}$ r(cdot) $end{document} is critical with respect to the Hardy-Littlewood-Sobolev inequality for variable exponents. We first consider the case where the perturbation begin{document}$ g(cdot ,cdot) $end{document} is subcritical and we distinguish between the superlinear and sublinear cases. In both situations we establish the existence of solutions and we prove the asymptotic behavior of low-energy solutions in the case of high perturbations. Next, we study the case where the nonlinearity begin{document}$ g(cdot ,cdot) $end{document} is critical. We prove the existence of solutions both for low and high perturbations and we establish asymptotic properties of low-energy solutions.

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引用次数: 2

Forward untangling and applications to the uniqueness problem for the continuity equation 前向解结及其在连续性方程唯一性问题中的应用

Discrete & Continuous Dynamical Systems - S

Pub Date : 2021-01-01 DOI: 10.3934/dcds.2020384

S. Bianchini, P. Bonicatto

We introduce the notion of forward untangled Lagrangian representation of a measuredivergence vector-measure ρ(1, b), where ρ ∈ M+(Rd+1) and b : Rd+1 → Rd is a ρ-integrable vector field with divt,x(ρ(1, b)) = μ ∈ M(R × Rd): forward untangling formalizes the notion of forward uniqueness in the language of Lagrangian representations. We identify local conditions for a Lagrangian representation to be forward untangled, and we show how to derive global forward untangling from such local assumptions. We then show how to reduce the PDE divt,x(ρ(1, b)) = μ on a partition of R+ × Rd obtained concatenating the curves seen by the Lagrangian representation. As an application, we recover known well posedeness results for the flow of monotone vector fields and for the associated continuity equation.

我们引入了测量收敛向量ρ(1, b)的前向解纠缠拉格朗日表示的概念，其中ρ∈M+(Rd+1)和b: Rd+1→Rd是一个ρ可积的向量场，其中divt,x(ρ(1, b)) = μ∈M(R × Rd):前向解纠缠形式化了拉格朗日表示语言中的前向唯一性概念。我们确定了拉格朗日表示向前解缠的局部条件，并展示了如何从这些局部假设中推导出全局向前解缠。然后，我们展示了如何减少PDE分割，x(ρ(1, b)) = μ上的分割，得到了连接由拉格朗日表示的曲线。作为一个应用，我们恢复了单调向量场的流动和相关的连续性方程的已知的完备性结果。

引用次数: 1

Observer-based control for a class of hybrid linear and nonlinear systems 一类线性和非线性混合系统的观测器控制

Discrete & Continuous Dynamical Systems - S

Pub Date : 2021-01-01 DOI: 10.3934/dcdss.2020376

A. Alessandri, F. Bedouhene, D. Bouhadjra, A. Zemouche, P. Bagnerini

An approach to output feedback control for hybrid discrete-time systems subject to uncertain mode transitions is proposed. The system dynamics may assume different modes upon the occurrence of a switching that is not directly measurable. Since the current system mode is unknown, a regulation scheme is proposed by combining a Luenberger observer to estimate the continuous state, a mode estimator, and a controller fed with the estimates of both continuous state variables and mode. The closed-loop stability is ensured under suitable conditions given in terms of linear matrix inequalities. Since complexity and conservativeness grow with the increase of the modes, we address the problem of reducing the number of linear matrix inequalities by providing more easily tractable stability conditions. Such conditions are extended to deal with systems having also Lipschitz nonlinearities and affected by disturbances. The effectiveness of the proposed approach is shown by means of simulations.

提出了一种具有不确定模态转换的混合离散系统的输出反馈控制方法。当发生不可直接测量的开关时，系统动力学可能呈现不同的模式。由于当前系统模式是未知的，因此提出了一种由Luenberger观测器估计连续状态、模态估计器和同时具有连续状态变量和模态估计的控制器相结合的调节方案。在线性矩阵不等式给出的适当条件下，保证了闭环的稳定性。由于复杂性和保守性随着模态的增加而增加，我们通过提供更容易处理的稳定性条件来解决减少线性矩阵不等式数量的问题。这些条件被推广到处理同样具有利普希茨非线性和受干扰影响的系统。仿真结果表明了该方法的有效性。

引用次数: 0

Stability and bifurcation analysis in a delay-induced predator-prey model with Michaelis-Menten type predator harvesting Michaelis-Menten型捕食者捕获延迟诱导捕食者-猎物模型的稳定性和分岔分析

Discrete & Continuous Dynamical Systems - S

Pub Date : 2021-01-01 DOI: 10.3934/dcdss.2020259

Ming Liu, Dongpo Hu, F. Meng

The present paper considers a delay-induced predator-prey model with Michaelis-Menten type predator harvesting. The existence of the nontrivial positive equilibria is discussed, and some sufficient conditions for locally asymptotically stability of one of the positive equilibria are developed. Meanwhile, the existence of Hopf bifurcation is discussed by choosing time delays as the bifurcation parameters. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out to support the analytical results.

本文考虑了具有Michaelis-Menten型捕食者捕获的延迟诱导捕食者-猎物模型。讨论了非平凡正平衡点的存在性，给出了其中一个正平衡点局部渐近稳定的充分条件。同时，通过选取时滞作为分岔参数，讨论了Hopf分岔的存在性。利用泛函微分方程的范式理论和中心流形定理，确定了Hopf分岔的方向和分岔周期解的稳定性。最后，进行了数值模拟来支持分析结果。

引用次数: 5

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