Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control by Lingling Zhang, Noriaki Yamazaki, Rui Guo

“…Firstly, by using a fixed point theorem of mixed monotone operator, we study positive solutions of the boundary value problem for impulsive differential equations with mixed monotone terms, and sufficient conditions for existence and uniqueness of positive solutions will be established. …”
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Intermittent Control for Synchronization of Discrete-Delayed Complex Cyber-Physical Networks under Mixed Attacks by Chaoqun Zhu, Xuan Jia, Pan Zhang

“…By utilizing the Lyapunov stability theorem, a novel synchronization control method is developed for the synchronization control of complex cyber-physical networks with mixed attacks. …”
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Dynamical Analysis of a Computer Virus Model with Delays by Juan Liu, Carlo Bianca, Luca Guerrini

“…Moreover the direction of the Hopf bifurcation and stability of the bifurcating period solutions are investigated by using the normal form theory and the center manifold theorem. Finally, numerical investigations are carried out to show the feasibility of the theoretical results.…”
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Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument by Kuo-Shou Chiu

“…Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. …”
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Adaptive Super-Twisting Sliding Mode Control for Mobile Robots Based on High-Gain Observers by Haitao Liu, Jianhao Nie, Jian Sun, Xuehong Tian

“…The stability of the closed-loop system is proved using the Lyapunov stability theorem. The effectiveness of the proposed control strategy is verified by simulation.…”
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Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of N... by Qiao-Li Dong, Yan-Ni Guo, Fang Su

“…Furthermore, we prove the strong convergence theorem of the studied iterative method. The results of this paper extend and improve the results of Ceng et al., (2008), W. …”
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Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model by Xueli Chen, Lishun Ren

“…The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. …”
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A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations by Yanli Zhou, Yonghong Wu, Xiangyu Ge, B. Wiwatanapataphee

“…In this paper, we construct a robust Taylor approximation scheme and then examine the convergence of the method in a weak sense. A convergence theorem for the scheme is established and proved. …”
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Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays by Nai-Wei Liu, Ting-Ting Kong

“…Finally, by using comparison theorem and the ω-limit set theory, we study the global asymptotic stability of the boundary equilibrium and the positive equilibrium, respectively. …”
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Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps by Tingting Ma, Xinzhu Meng, Zhengbo Chang

“…Using the comparison theorem of stochastic differential equations and asymptotic approaches, sufficient conditions for persistence in mean and extinction of three species are derived. …”
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Existence and optimal control of Hilfer fractional evolution equations by Zhou Mian, Zhou Yong, He Jia Wei, Liang Yong

“…The first part focuses on analyzing the existence and uniqueness of the mild solution using the fixed point theorem and semigroup theory. In the second part, an optimal control problem that admits an optimal pair is considered. …”
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Treatment for regularity of the Navier-Stokes equations based on Banach and Sobolev functional spaces coupled to anisotropic viscosity for analysis of vorticity transport by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales

“…Using the Banach and Sobolev functional spaces, we developed a new theorem that points out a path towards the creation of an anisotropic viscosity model, formulated in the present work. …”
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Approximation by Genuine q-Bernstein-Durrmeyer Polynomials in Compact Disks in the Case q>1 by Nazim I. Mahmudov

“…Quantitative estimates of the convergence, the Voronovskaja-type theorem, and saturation of convergence for complex genuine q-Bernstein-Durrmeyer polynomials attached to analytic functions in compact disks are given. …”
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Phillips-Type q-Bernstein Operators on Triangles by Asif Khan, M. S. Mansoori, Khalid Khan, M. Mursaleen

“…The purpose of the paper is to introduce a new analogue of Phillips-type Bernstein operators Bm,qufu,v and Bn,qvfu,v, their products Pmn,qfu,v and Qnm,qfu,v, their Boolean sums Smn,qfu,v and Tnm,qfu,v on triangle Th, which interpolate a given function on the edges, respectively, at the vertices of triangle using quantum analogue. Based on Peano’s theorem and using modulus of continuity, the remainders of the approximation formula of corresponding operators are evaluated. …”
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Infinitely Many Solutions for a Superlinear Fractional p-Kirchhoff-Type Problem without the (AR) Condition by Xiangsheng Ren, Jiabin Zuo, Zhenhua Qiao, Lisa Zhu

“…We only consider the non-Ambrosetti-Rabinowitz condition to prove our results by using the symmetric mountain pass theorem.…”
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Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function by Bing-Wei Niu, Jian-Ping Sun, Qiu-Yan Ren

“…Although the corresponding Green's function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on f by using the two-fixed-point theorem due to Avery and Henderson. An example is also included to illustrate the main results obtained.…”
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Sound Radiation due to Modal Vibrations of a Spherical Source in an Acoustic Quarterspace by Seyyed M. Hasheminejad, Mahdi Azarpeyvand

“…The formulation utilizes the appropriate wave field expansions along with the translational addition theorem for spherical wave functions in combination with the classical method of images to develop a closed-form solution in form of infinite series. …”
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Indoor EKF localization algorithm based on RFID carrier phase by Liangbo XIE, Xixi LIU, Yong WANG, Mu ZHOU, Zengshan TIAN

“…In order to solve the problem of low localization accuracy caused by indoor environment interference in the existing UHF RFID localization methods, an indoor extended Kalman filter (EKF) localization algorithm based on frequency hopping assisted RFID carrier phase was proposed.The virtual large bandwidth obtained by frequency hopping was used for rough distance estimation to realize multipath suppression, and the reliable dual frequency point selection and parameter optimization were completed through the phase after multipath suppression.Finally, EKF algorithm was used to realize high-precision and fast localization.Experimental results show that the average localization error of the proposed algorithm is 9.35 cm, and the real-time performance of the localization solution is nearly 10 times higher than the traditional integer solution method based on Chinese remainder theorem (CRT).…”
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Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters by Zhenguo Luo

“…By applying the fixed point theorem, we derive some new criteria for the existence of multiple positive periodic solutions for two kinds of  n-dimension periodic impulsive functional differential equations with multiple delays and two parameters: xi′(t)=ai(t)xi(t)-λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e., t>0, t≠tk, k∈Z+, xi(tk+)-xi(tk-)=μcikxi(tk), i=1,2,…,n, k∈Z+, and xi′(t)=-ai(t)xi(t)+λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e., t>0, t≠tk, k∈Z+, xi(tk+)-xi(tk-)=μcikxi(tk), i=1,2,…,n, k∈Z+. …”
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Full Wave Modeling of Array Structures Using Generalized Single-Source Tangential Equivalence Principle Algorithm by Hanru Shao, Jianfeng Dong, Jun Hu

“…This scheme can also reduce the number of unknowns by half via the extinction theorem and keep the good accuracy by using tangential field projection. …”
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