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The novelty of this paper is that, based on Mawhin's continuation theorem, we present some sufficient conditions that ensure that there is at least one solution to a particular kind of a boundary value problem with the p-Laplacian and generalized fractional Caputo derivative. [ABSTRACT FROM AUTHOR]

By means of Mawhin's continuation theorem of coincidence degree theory and Lyapunov function, some simple sufficient conditions are obtained for the existence and stability of a unique positive almost periodic solution of a delayed Lotka-Volterra recurrent neural networks. To a certain extent, the work in this paper corrects the defect of a recent paper. Finally, an example and simulations are given to illustrate the feasibility and effectiveness of the main result. [ABSTRACT FROM AUTHOR]

In this paper, existence and uniqueness of periodic solutions of second‐order semilinear impulsive differential equations are obtained. Some sufficient conditions that guarantee the existence of periodic solutions to second‐order linear nonhomogeneous impulsive differential equations are obtained. In addition, by using the appropriate fixed theorem and the theory of coincidence degree, some conditions ensuring the existence and uniqueness of periodic solution to second‐order semilinear impulsive differential systems are derived. Finally, some examples are provided to illustrate the availability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we study a general nonautonomous model for bacterial dynamics in rivers. The mathematical model is represented by a nonautonomous system of nonlinear ordinary differential equations. We show the existence of a bounded positive invariant and attracting set. By using the Lyapunov function method, we establish global stability of steady‐state solutions of the associated autonomous system. Second, the existence of positive periodic solutions of the nonautonomous system is proven using a continuation theorem based on coincidence degree theory. [ABSTRACT FROM AUTHOR]

In this paper we are interested in the existence of solutions for the following boundary value problem at resonance on the half-line where f : R + × R 2 → R is q-Carathéodory, g : R + → R + is a nondecreasing function with g (0) = 0 under the resonance condition g (∞) = 1 . The coincidence degree theory of Mawhin [17] is used to establish the existence of at least one solution for the posed problem. [ABSTRACT FROM AUTHOR]

Online group streaming feature selection, as an essential online processing method, can deal with dynamic feature selection tasks by considering the original group structure information of the features. Due to the fuzziness and uncertainty of the feature stream, some existing methods are unstable and yield low predictive accuracy. To address these issues, this paper presents a novel online group streaming feature selection method (FNE-OGSFS) using fuzzy neighborhood entropy-based uncertainty measures. First, a separability measure integrating the dependency degree with the coincidence degree is proposed and introduced into the fuzzy neighborhood rough sets model to define a new fuzzy neighborhood entropy. Second, inspired by both algebra and information views, some fuzzy neighborhood entropy-based uncertainty measures are investigated and some properties are derived. Furthermore, the optimal features in the group are selected to flow into the feature space according to the significance of features, and the features with interactions are left. Then, all selected features are re-evaluated by the Lasso model to discard the redundant features. Finally, an online group streaming feature selection algorithm is designed. Experimental results compared with eight representative methods on thirteen datasets show that FNE-OGSFS can achieve better comprehensive performance. [ABSTRACT FROM AUTHOR]

In this paper, we consider a kind of stage-structured predator-prey systems with two predators and general functional responses. By applying the comparison theorem, Lyapunov functional and Mawhin's continuation theorem of coincidence degree theory, this paper gives some new sufficient conditions for the uniform persistence, globally asymptotical stability and almost-periodic solutions for the above system. Two examples and numerical simulations are provided to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, for double row angular contact ball bearing, a five-degrees-of-freedom bearing analysis model based on quasi-statics is proposed. This model is used to study the influence of structural parameters and service conditions on the tilt angle and limit tilt angle of the bearing. The results show that the radial clearance will increase the ultimate tilt angle. The coincidence degree between the roller and the inner raceway will reduce the ultimate tilt angle, but the coincidence degree between the roller and the outer raceway has the opposite effect. The increase in the external load of the bearing will increase the tilt angle. The moment load has the greatest effect on the tilt angle. The rotation speed of the bearing has no effect on the tilt angle. The coincidence degree between the roller and the raceway will reduce the tilt angle; furthermore, the influence of the coincidence degree between roller and different ring on the tilt angle is also different when different rings are fixed. The tilt angle will decrease with the increase of the initial contact angle, and this effect is more and more obvious. The fixation of different ring has no effect on this influence. [ABSTRACT FROM AUTHOR]

This paper is concerned with the dynamics of a three-level food-chain model with time delays. By means of Mawhin's continuation theorem of coincidence degree theory, we investigate the existence of positive almost periodic solutions in a three-level food-chain model with time delays. A set of sufficient conditions for the existence of at least one positive almost periodic solution of the model is obtained. In addition, the global asymptotical stability of the almost periodic solution of the above model is also studied. Finally, two examples and simulations are also given to illustrate the main results in this paper. [ABSTRACT FROM AUTHOR]

Recently, the higher order averaging method for studying periodic solutions of both Lipschitz diferential equations and discontinuous piecewise smooth diferential equations was devel- oped in terms of the Brouwer degree theory. Between the Lipschitz and the discontinuous piecewise smooth diferential equations, there is a huge class of diferential equations lacking in a higher order analysis on the existence of periodic solutions, namely, the class of continuous non-Lipschitz diferen- tial equations. In this paper, based on the degree theory for operator equations, we perform a higher order analysis of continuous perturbed diferential equations and derive sufcient conditions for the existence and uniform convergence of periodic solutions for such systems. We apply our results to study continuous non-Lipschitz higher order perturbations of a harmonic oscillator. [ABSTRACT FROM AUTHOR]

The paper computes the Brouwer degree of some classes of homogeneous polynomials defined on quaternions and applies the results, together with a continuation theorem of coincidence degree theory, to the existence and multiplicity of periodic solutions of a class of systems of quaternionic valued ordinary differential equations. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'. [ABSTRACT FROM AUTHOR]

In this paper, by applying Mawhin's continuation theorem of coincidence degree theory, we consider the following fishing model with harvesting term ... and obtain some new sufficient conditions for the existence of at least two positive almost periodic solutions for the model. In addition, the local asymptotical stability of the model is also discussed. An example is employed to illustrate the result in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of solutions for Riemann-Stieltjes integral boundary value problems of fractional differential equation by using Mawhin's coincidence degree theory. An example is given to show the application of our result. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the existence and convergence of solutions to periodic boundary value problems for one‐dimensional Kirchhoff equation. By employing analytical skills and the coincidence degree method, some new results are obtained, which enrich and generalize the previous results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of periodic solution of a delayed predator-prey model with M -predators and N -preys over the time scales. We derive sufficient conditions for the existence of a periodic solution with the help of continuation theorem of coincidence degree theory. At the end, we give an example with numerical simulations to illustrate our analytical findings. [ABSTRACT FROM AUTHOR]

The existence of a solution for a second-order p-Laplacian boundary value problem at resonance with two dimensional kernel will be considered in this paper. A semi-projector, the Ge and Ren extension of Mawhin's coincidence degree theory, and algebraic processes will be used to establish existence results, while an example will be given to validate our result. [ABSTRACT FROM AUTHOR]

In this paper, a class of generalised inertial competitive neural networks with time-varying delays is proposed. The existence and global exponential stability of anti-periodic solutions for this class of neural networks are investigated. By using a continuation theorem of coincidence degree theory, the Wirtinger inequality and constructing an appropriate Lyapunov function, some sufficient conditions are derived to guarantee the existence, uniqueness, and global exponential stability of anti-periodic solutions for the considered networks. Our results are completely new. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a class of quaternion-valued cellular neural networks with time-varying transmission delays and leakage delays. By applying a continuation theorem of coincidence degree theory and the Wirtinger inequality as well as constructing a suitable Lyapunov functional, sufficient conditions are derived to ensure the existence and global exponential stability of anti-periodic solutions via direct approaches. Our results are completely new. Finally, numerical examples are also provided to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of quaternion-valued inertial neural networks with time-varying delays. First, by applying a continuation theorem of coincidence degree theory, we establish the existence of anti-periodic solutions of the considered neural networks. Second, by choosing a proper variable substitution, we transform the neural networks into a system of first order differential equations, and by constructing a suitable Lyapunov function, we derive a set of sufficient conditions ensuring the global exponential stability of the system. Finally, we give two examples to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, we study an almost periodic nonautonomous bi-directional consumer-resource system described by a facultative mutualism model with time delays. By using Mawhin's continuation theorem of coincidence degree theory and constructing a suitable Lyapunov functional, some easily verifiable conditions are obtained for the existence and global asymptotic stability of positive almost periodic solutions of the above system. Some example and numerical simulations are provided to illustrate the main results of this paper. Finally, a conclusion is also given to discuss how the parameters of the system influence the existence and global asymptotic stability of positive almost periodic oscillations. [ABSTRACT FROM AUTHOR]

In this paper, a non-autonomous SIR epidemic model with almost periodic transmission rate and a constant removal rate is considered. By means of Mawhin's continuous theorem of coincidence degree, some new sufficient conditions for the existence and multiplicity of positive almost periodic solutions to the model are established. Further, the global asymptotical stability of positive almost periodic solution of the model is also investigated by constructing a suitable Lyapunov functional. Finally, some examples and numerical simulations are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of periodic solutions of modified version of the Leslie-Gower predator-prey model with Holling-type II functional response in the presence of Michaelis-Menten type prey harvesting over a time scale. Sufficient conditions for the existence of periodic solutions are derived by using the continuation theorem of coincidence degree theory. The condition we obtain is easily verifiable and not much restricted. [ABSTRACT FROM AUTHOR]

By means of a fixed point theorem of coincidence degree theory, sufficient conditions for the multiplicity of positive almost periodic solutions to a delayed harvesting predator-prey model with modified Leslie-Gower Hollingtype II schemes are established. The method used in this paper provides a possible method to study the multiplicity of positive almost periodic solutions of the models in biological populations. Finally, an example and computer simulations are given to illustrate the feasibility and effectiveness of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the study of the existence of positive solutions for the following nonlinear boundary value problem on the half-line: { - u ′′ ⁢ (x) = q ⁢ (x) ⁢ f ⁢ (x , u , u ′) , x ∈ (0 , + ∞) , u ′ ⁢ (0) = u ′ ⁢ (+ ∞) = 0 , \left\{\begin{aligned} \displaystyle-u^{\prime\prime}(x)&\displaystyle=q(x)f(x% ,u,u^{\prime}),&&\displaystyle x\in(0,+\infty),\\ \displaystyle u^{\prime}(0)&\displaystyle=u^{\prime}(+\infty)=0,\end{aligned}\right. where q : ℝ + → ℝ + {q:\mathbb{R^{+}}\rightarrow\mathbb{R^{+}}} is a positive measurable function such that ∫ 0 + ∞ q ⁢ (x) ⁢ 𝑑 x = 1 {\int_{0}^{+\infty}q(x)\,dx=1} and f : ℝ + × ℝ 2 → ℝ {f:\mathbb{R}^{+}\times\mathbb{R}^{2}\rightarrow\mathbb{R}} is q-Carathéodory. [ABSTRACT FROM AUTHOR]

In this paper, quaternion-valued high-order Hopfield neural networks (QVHHNNs) with time-varying delays are considered. Theoretically, a QVHHNN can be separated into four real-valued systems, forming an equivalent real-valued system. By using a novel continuation theorem of coincidence degree theory and constructing an appropriate Lyapunov function, some sufficient conditions are derived to guarantee the existence and global exponential stability of anti-periodic solutions for QVHHNN, which are new and complement previously known results. [ABSTRACT FROM AUTHOR]

This paper discusses a class of impulsive neural networks with the variable delay and complex deviating arguments. By using Mawhin's continuation theorem of coincidence degree and the Halanay-type inequalities, several sufficient conditions for impulsive neural networks are established for the existence and globally exponential stability of periodic solutions, respectively. Furthermore, the obtained results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results. [ABSTRACT FROM AUTHOR]

By using some analytical techniques, modified inequalities and Mawhin's continuous theorem of coincidence degree theory, some simple sufficient conditions for the existence of at least one positive almost periodic solution of a generalized Mackey-Glass model of respiratory dynamics are obtained. Further, the global attractivity of positive almost periodic solution of the above model is also studied. To the best of the author's knowledge, so far, the result of this paper is completely new. Finally, three examples are given to illustrate the main results in this paper. [ABSTRACT FROM AUTHOR]

In this paper, using Mawhin's continuation theorem of the coincidence degree theory, we obtain some sufficient conditions for the existence of positive almost periodic solutions for a class of delay discrete models with Allee-effect. [ABSTRACT FROM AUTHOR]

In this paper, we consider a delayed Hassell-Varley-type predator-prey model with harvesting on prey. By means of Mawhin's continuation theorem of coincidence degree theory, some new sufficient conditions are obtained for the existence of at least two positive almost periodic solutions for the aforementioned model. To the best of the author's knowledge, so far, the result of this paper is completely new. An example is employed to illustrate the result of this paper. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

By using some new analytical techniques, modified inequalities and Mawhin's continuous theorem of coincidence degree theory, some new sufficient conditions for the existence of positive almost periodic solutions to a mutualism model with bounded and unbounded delays are obtained. Further, the boundedness and global asymptotic stability have been studied. To the best of the author's knowledge, so far, the result of this paper is completely new. The work of this paper extends and improves some results in recent years. Finally, some examples are given to illustrate the main results in this paper. [ABSTRACT FROM AUTHOR]

We prove that the superlinear indefinite equation where and is a -periodic sign-changing function satisfying the (sharp) mean value condition , has positive subharmonic solutions of order for any large integer , thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467-477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré-Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it). [ABSTRACT FROM AUTHOR]

This paper presents a new technique to investigate the existence of solutions to fractional three-point boundary value problems at resonance in a Hilbert space. Based on the proposed method, the restricted conditions A²ξ1α-2 = Aξα-1 and A²ξ2α-2 = I on the operator A, which have been used in [18], are removed. It is shown that the system under consideration admits at least one solution by applying coincidence degree theory. Finally, an illustrative example is presented. [ABSTRACT FROM AUTHOR]

In this paper, we use the coincidence degree theory to research the odd order delay differential equation a( t) x)( t) + b( t) x( t) + g( t,x( t− τ( t))) = p( t), and we obtain the sufficient conditions for the existence of periodic solutions, which improves and generalizes some related results in the literatures. [ABSTRACT FROM AUTHOR]

In this paper, a kind of Liénard equation with multiple deviating arguments of the form is considered. By using coincidence degree theory, some criteria are obtained to guarantee the existence and uniqueness of periodic solutions of this equation. The obtained results are also valid and new for the problem discussed in the previous literature. [ABSTRACT FROM AUTHOR]

In this paper we discuss the existence of positive T-periodic solutions for the following second order differential equation where f, g:ℝ+=(0,+∞)→ℝ are continuous functions, g has a repulsive singularity at the origin and c( t) is a continuous T-periodic function. The novelty of the present article is that for the first time we show that a weakly repulsive singularity enables the achievement of a new existence criterion of positive T-periodic solutions through a basic application of the coincidence degree theory. Recent results in the literature are generalized and significantly improved. [ABSTRACT FROM AUTHOR]

In this paper, by using the continuation theorem of coincidence degree theory we study the existence of periodic solution for a two-species ratio-dependent predator-prey system with time-varying delays and Machaelis–Menten type functional response on time scales. Some new results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we establish the existence of at least two positive periodic solutions for a discrete time delayed predator-prey system with harvesting terms. An example is given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, by using the method of coincidence degree theory, we explore the existence of periodic solutions for a cooperative ecological model on time scales. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a discrete-time non-autonomous predator-prey system with the Beddington-DeAngelis functional response. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable sufficient criteria are established for the existence of positive periodic solutions. [ABSTRACT FROM AUTHOR]

This paper gives new sufficient conditions for the existence of periodic solutions of a second order non-autonomous differential system by using Mawhin's coincidence degree theory and Brousk's theorem. These results substantially extend and improve the corresponding results in the literatures [1,6,7]. [ABSTRACT FROM AUTHOR]

Applying coincidence degree theory of Mawhin, this paper is concerned with existence result for a coupled fractional differential systems with Riemann-Stieltjes integral boundary value conditions. An example is also given to illustrate the main result. [ABSTRACT FROM AUTHOR]

By using some analytical techniques, modified inequalities and Mawhin's continuous theorem of coincidence degree theory, some sufficient conditions for the existence of positive almost periodic solutions to a class of Gilpin-Ayala competition model of phytoplankton allelopathy are established. Further, by constructing a suitable Lyapunov functional, the global asymptotical stability of almost periodic solution for the model is also studied. The work of this paper extends and improves some results in recent years. Finally, some examples and simulations are given to illustrate the main results in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the solvability of a fully nonlinear third-order m-point boundary value problem at resonance posed on the half line. The nonlinearity which depends on the first and the second derivatives satisfies a sublinear-like growth condition. Our main existence result is based on Mawhin's coincidence degree theory. An illustrative example of application is included. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of solutions for fractional p-Laplacian differential equation with multipoint boundary conditions at resonance on an infinite interval. Under an appropriate compactness criterion, we make use the coincidence degree theory to establish the existence of solutions to the above-mentioned equation. An example is given to illustrate the obtained result. [ABSTRACT FROM AUTHOR]

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This paper is concerned with a periodic nonlinear competition model governed by impulsive differential equation with infinitely distributed delays and feedback controls. By means of coincidence degree theory and Lyapunov functional, a set of sufficient criteria are obtained to guarantee the existence and globally asymptotic stability of a unique positive periodic solution of the model. Furthermore, applying our main results to some important competition models which have been well studied in the literature, we establish some new criteria to supplement and generalize some well-known results. [ABSTRACT FROM AUTHOR]

We investigate the existence of solutions for coupled systems of fractional p-Laplacian quasilinear boundary value problems at resonance given by the Atangana–Baleanu–Caputo (shortly, ABC) derivatives formulations are based on the well-known Mittag-Leffler kernel utilizing Ge’s application of Mawhin’s continuation theorem. Examples are provided to demonstrate our findings. [ABSTRACT FROM AUTHOR]

Overf the last few years, by utilizing Mawhin’s continuation theorem of coincidence degree theory and Lyapunov functional, many scholars have been concerned with the global asymptotical stability of positive periodic solutions for the non-linear ecosystems. In the real world, almost periodicity is usually more realistic and more general than periodicity, but there are scarcely any papers concerning the issue of the global asymptotical stability of positive almost periodic solutions of non-linear ecosystems. In this paper we consider a kind of delayed two-species competitive model with stage structure. By means of Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the existence of at least one positive almost periodic solutions for the above model with nonnegative coefficients. Furthermore, the global asymptotical stability of positive almost periodic solution of the model is also studied. The work of this paper extends and improves some results in recent years. An example and simulations are employed to illustrate the main results of this paper.

By means of Mawhin’s continuation theorem of coincidence degree theory, some new and simple sufficient conditions are obtained for the existence of at least one positive almost periodic solution for a class of delayed Lasota-Wazewska model with nonnegative coefficients. Further, by some important inequalities and Lyapunov functional, the permanence and global asymptotical stability of the model have been studied. The main result of this paper improves some conditions of the result in [Z.D. Huang, S.H. Gong, L.J. Wang, Positive almost periodic solution for a class of Lasota-Wazewska model with multiple timing-varing delays, Comput. Math. Appl. 61 (2011) 755-760]. Two examples and numerical simulations are employed to illustrate the main result in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence and global exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg BAM neural networks on time scales. Applying the method of coincidence degree and constructing some suitable Lyapunov functional, we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg BAM neural networks on time scales. Moreover, we give an example to illustrate the results obtained. [ABSTRACT FROM AUTHOR]