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In this paper, a class of neutral delayed Lotka–Volterra competition system with impulsive perturbations is investigated. We explore the existence of positive periodic solutions of the system by using Mawhin coincidence degree theory and some analytical approaches. From our results, we find that a part of n species of the system is driven to extinction due to competition exclusion and weak adaption to environment characterized by impulsive perturbations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the following sequential fractional differential equationwhere is the Caputo fractional derivative, and . By the coincidence degree continuation theorem, we get some existence results about the boundary value problem at resonance. [Copyright &y& Elsevier]

Abstract: This paper is devoted to impulsive periodic Gause-type predator–prey systems with monotonic or non-monotonic numerical responses. With the help of a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of positive periodic solutions. As corollaries, some applications are listed. In particular, our results improve and generalize some known ones. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the existence of solutions for a three-point boundary value problem of fractional differential equations with nonlinear growth. By using the coincidence degree theory, we present a existence result at resonance case. [Copyright &y& Elsevier]

Abstract: In this paper, we propose an impulsive semi-ratio-dependent predator–prey model with dispersion and time delays. By applying the continuation theorem of coincidence degree theory, we establish a set of sufficient conditions on the existence of at least one positive periodic solution. The result not only improves but also generalizes that for the case without pulses. [Copyright &y& Elsevier]

Abstract: The main aim of this paper is to study the existence and global exponential stability of periodic solution for high-order bidirectional associative memory (BAM) neural networks with and without impulses. Easily verifiable sufficient conditions are established. The method is based on coincidence degree theory as well as a priori estimates and Lyapunov functional. It is shown that the convergence characteristics of periodic solution for the impulsive system are preserved by the corresponding nonimpulsive system with some restriction imposed on the impulse effect. Numerical simulation results are given to support the theoretical predictions. [Copyright &y& Elsevier]

Abstract: The main purpose of this paper is to show how the coincidence degree theory can be used to obtain almost periodic solutions for single population model with almost periodic coefficients. Some sufficient conditions are obtained for checking the existence, uniqueness and stability of almost periodic solution. The analysis generalizes the results corresponding to the periodic case of the single population model. [Copyright &y& Elsevier]

Abstract: In this paper, we establish a periodic delayed predator–prey system according to two types of single-species growth population models with delay. By using some analysis methods, easily verifiable sufficient conditions for the existence and global asymptotic stability of positive periodic solution of the above system are derived. Some previous results are generalized and improved. Biological interpretations on the main results are also given. [Copyright &y& Elsevier]

Abstract: In this paper, we study the asymptotic behavior of solutions in nonautonomous predator–prey patchy system with Beddington-type functional response. It is proved that the system is permanent under some appropriate conditions. Furthermore, if the system is a(n) (almost) periodic one, a set of easily verifiable sufficient conditions which guarantee the existence, uniqueness and global asymptotic stability of a positive (almost) periodic solutions of system are obtained. [Copyright &y& Elsevier]

In this paper, several sufficient conditions are investigated for the existence of positive periodic solutions of a general neutral Lotka–Volterra system with unbounded delays by using the theory of coincidence degree. Our results extend and improve existing results, and have further applications in population dynamics. [Copyright &y& Elsevier]

In this paper, we consider the following second order ordinary differential equation(1.1)x′′=f(t,x(t),x′(t))+e(t), t∈(0,1),subject to one of the following boundary value conditions: (1.2)x(0)=∑i=1m−2αix(ξi), x(1)=∑j=1n−2βjx(ηj),(1.3)x(0)=∑i=1m−2αix(ξi), x′(1)=∑j=1n−2βjx′(ηj),(1.4)x′(0)=∑i=1m−2αix′(ξi), x(1)=∑j=1n−2βjx(ηj),where αi (1&les;i&les;m−2), βj (1&les;j&les;n−2)∈R, 0<ξ1<ξ2<⋯<ξm−2<1, 0<η1<η2<⋯<ηn−2<1. When all the αis have no the same sign and all the βjs have no the same sign, some existence results are given for (1.1) with boundary conditions (1.2)–(1.4) at resonance case. We also give some examples to demonstrate our results. [Copyright &y& Elsevier]

In this paper, we consider the following second order ordinary differential equation:(1.1)x″=f(t,x(t),x′(t))+e(t), t∈(0,1),subject to one of the following boundary value conditions:(1.10)x(0)=αx(ξ), x(1)=∑j=1n−2βjx(ηj),(1.11)x(0)=αx(ξ), x′(1)=∑j=1n−2βjx′(ηj),(1.12)x′(0)=αx′(ξ), x(1)=∑j=1n−2βjx(ηj),(1.13)x′(0)=αx′(ξ), x′(1)=∑j=1n−2βjx′(ηj),where α,βj(1&les;j&les;n−2)∈R, 0<η1<η2<⋯<ηn−2<1, 0<ξ<1. When all the βj’s have no same sign, some existence results are given for (1.1) with boundary conditions (1.10)–(1.13) at resonance case. We also give some examples to demonstrate our results. [Copyright &y& Elsevier]