Dynamic Analysis of an SEIR Model with Distinct Incidence for Exposed and Infectives by Junhong Li, Ning Cui

“…By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. …”
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The Solvability and Optimal Controls for Some Fractional Impulsive Equation by Xianghu Liu, Zhenhai Liu, Jiangfeng Han

“…Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. …”
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Dynamical Behavior of a Stochastic Ratio-Dependent Predator-Prey System by Zheng Wu, Hao Huang, Lianglong Wang

“…This paper is concerned with a stochastic ratio-dependent predator-prey model with varible coefficients. By the comparison theorem of stochastic equations and the Itô formula, the global existence of a unique positive solution of the ratio-dependent model is obtained. …”
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On Complete Convergence and Strong Law for Weighted Sums of i.i.d. Random Variables by Pingyan Chen, Xiaofang Ma, Soo Hak Sung

“…We improve and generalize the result of Stout (1974, Theorem 4.1.3). In particular, the sharp moment conditions are obtained and some well-known results can be obtained as special cases of the main result. …”
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Hopf Bifurcations and Oscillatory Patterns of a Homogeneous Reaction-Diffusion Singular Predator-Prey Model by Zhenhua Bao, He Liu

“…By using the abstract simplified Hopf bifurcation theorem due to Yi et al. 2009, we performed detailed Hopf bifurcation analysis of this particular pattern formation system. …”
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Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle by Huanhuan Tian, Maoan Han

“…We also obtain formulas for the first coefficients appearing in the expansions and then establish a bifurcation theorem on the number of limit cycles. As an application example, we give a lower bound of the maximal number of limit cycles for a polynomial system of Liénard type.…”
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Block Empirical Likelihood for Semiparametric Varying-Coefficient Partially Linear Errors-in-Variables Models with Longitudinal Data by Yafeng Xia, Hu Da

“…And the nonparametric version of Wilk’s theorem is derived under mild conditions. Simulations are carried out to access the performance of the proposed procedure.…”
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Global Exponential Stability of Positive Pseudo-Almost-Periodic Solutions for a Model of Hematopoiesis by Junxia Meng

“…Under suitable assumptions, and by using fixed point theorem, sufficient conditions are given to ensure that all solutions of this model converge exponentially to the positive pseudo almost periodic solution for the considered model. …”
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Analysis of a New Quadratic 3D Chaotic Attractor by Shahed Vahedi, Mohd Salmi Md Noorani

“…We finally prove existence of this chaotic attractor theoretically using Shil’nikov theorem and undetermined coefficient method.…”
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Empirical Likelihood for Partial Parameters in ARMA Models with Infinite Variance by Jinyu Li, Wei Liang, Shuyuan He

“…Also, the paper proves a nonparametric version of Wilks’s theorem. Furthermore, we conduct a simulation to illustrate the performance of the proposed method.…”
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Existence of Solution via Integral Inequality of Volterra-Fredholm Neutral Functional Integrodifferential Equations with Infinite Delay by Kishor D. Kucche, Machindra B. Dhakne

“…To obtain a priori bounds of solutions required in Krasnoselski-Schaefer type fixed point theorem, we have used an integral inequality established by B. …”
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A generalized formula of Hardy by Geoffrey B. Campbell

“…Hardy originally gave such formulae as ours in early work on gap power series which led to his and Littlewood's High Indices Theorem. Over a decade ago, Mahler and then others proved results on irrationality of decimal fractions applicable to types of functions we consider.…”
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Contractibility of Fixed Point Sets of Mean-Type Mappings by S. Iampiboonvatana, P. Chaoha

“…We establish a convergence theorem and explore fixed point sets of certain continuous quasi-nonexpansive mean-type mappings in general normed linear spaces. …”
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Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain by Zhanrong Hu, Zhen Jin

“…Combining the exponential dichotomy of evolution family, composition theorems for almost automorphic functions with Banach fixed point theorem, we establish new existence and uniqueness theorems for almost automorphic mild solutions to neutral parabolic nonautonomous evolution equations with nondense domain. …”
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Periodic Solutions and Exponential Stability of a Class of Neural Networks with Time-Varying Delays by Yingxin Guo, Mingzhi Xue

“…Employing fixed point theorem, we make a further investigation of a class of neural networks with delays in this paper. …”
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Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation by Jia Wei, Xiaoling Han, Fumei Ye

“…As applications, we give some examples to illustrate the application of these theorems.…”
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A New Approach to the Approximation of Common Fixed Points of an Infinite Family of Relatively Quasinonexpansive Mappings with Applications by Wei-Qi Deng

“…A strong convergence theorem without the stronger assumptions of the AKTT condition and the ∗AKTT condition imposed on the involved mappings is established in the framework of Banach space. …”
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Existence of Solutions for a Class of Coupled Fractional Differential Systems with Nonlocal Boundary Conditions by Tingting Qi, Yansheng Liu, Yujun Cui

“…Applying Schauder fixed point theorem and Leray-Schauder nonlinear alternative theory, this paper is concerned with the existence of solutions to coupled fractional differential systems with fractional integral boundary value conditions. …”
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Exponential Stability of Periodic Solutions for Inertial Type BAM Cohen-Grossberg Neural Networks by Chunfang Miao, Yunquan Ke

“…Second, some sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov functional and using differential mean value theorem and inequality technique. Finally, two examples are given to illustrate the effectiveness of the results.…”
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Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate by Kai Zhou, Qi-Ru Wang

“…By using the cross-iteration method and Schauder’s fixed point theorem, we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions. …”
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