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Abstract: In this work, we use the coincidence degree theory to establish new results on the existence and uniqueness of -periodic solutions for a kind of Liénard equation with a deviating argument of the form [Copyright &y& Elsevier]

Abstract: In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of -periodic solutions for the second order neutral functional differential equation of the form [Copyright &y& Elsevier]

Abstract: Without assuming the boundedness, monotonicity, and differentiability of activation functions and any symmetry of interconnections, we establish some sufficient conditions for the global exponential stability of a unique equilibrium and the existence of periodic solution for the Cohen–Grossberg neural network with time-varying delays. Brouwer''s fixed point theorem, matrix theory, a continuation theorem of the coincidence degree and inequality analysis are employed. Our results are all independent of the delays and maybe more convenient to design a circuit network. [Copyright &y& Elsevier]

Abstract: In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the first order neutral functional differential equation of the form [Copyright &y& Elsevier]

Abstract: In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Rayleigh equation with a deviating argument of the form [Copyright &y& Elsevier]

Abstract: By applying the continuation theorem of coincidence degree theory, we establish the existence of 2π-periodic solutions for a class of nonlinear nth order differential equations with delays. [Copyright &y& Elsevier]

Abstract: Employing Brouwer''s fixed point theorem, matrix theory, a continuation theorem of the coincidence degree and inequality analysis, the authors make a further investigation of a class of cellular neural networks with delays (DCNNs) in this Letter. A family of sufficient conditions are given for checking global exponential stability and the existence of periodic solutions of DCNNs. These results have important leading significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. Our results extend and improve some earlier publications. [Copyright &y& Elsevier]

In this Letter, we study BAM (bidirectional associative memory) networks with variable coefficients. By some spectral theorems and a continuation theorem based on coincidence degree, we not only obtain some new sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution but also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Moreover, these conclusions are presented in terms of system parameters and can be easily verified for the globally Lipschitz and the spectral radius being less than 1. Therefore, our results should be useful in the design and applications of periodic oscillatory neural circuits for neural networks with delays. [Copyright &y& Elsevier]

Abstract: With the help of the continuation theorem of the coincidence degree, a priori estimates, and differential inequalities, the authors make a further investigation of a class of Rayleigh equation with two deviating arguments of the form Some new results on the existence of -periodic solutions for such a system are established. Our work generalizes and improves some earlier publications. [Copyright &y& Elsevier]