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In this paper, the existence of positive solutions of the following third-order three-point boundary value problem with p-Laplacian {(Φp(u"(t)))' + f(t, u(t)) = 0, t (0, 1), u(0) = au(η), u(1) = au(η), u"(0) = 0, is studied, where Φp(s) = |s|p-2s, p > 1. By using the fixed point index method, we establish sufficient conditions for the existence of at least one or at least two positive solutions for the above boundary value problem. The main result is demonstrated by providing an example as an application. [ABSTRACT FROM AUTHOR]

In this paper, we prove that a predator-prey model with sigmoid functional response and logistic growth for the prey has a unique stable limit cycle, if the equilibrium point is locally unstable. This extends the results of the literature where it was proved that the equilibrium point is globally asymp-totically stable, if it is locally stable. For the proof, we use a combination of three versions of Zhang Zhifen's uniqueness theorem for limit cycles in Liénard systems to cover all possible limit cycle configurations. This technique can be applied to a wide range of differential equations where at most one limit cycle occurs. [ABSTRACT FROM AUTHOR]

In this paper, we investigate Lie symmetry group, optimal system, exact solutions and conservation laws of modified hyperbolic geometric flow via Lie symmetry method. Then, conservation laws of modified hyperbolic geometric flow are obtained by applying Ibragimov method. [ABSTRACT FROM AUTHOR]

In this paper, the existence of solutions to a class of fractional differential equations ... is obtained by an efficient and simple monotone iteration method. At first, the existence of a solution to the problem above is guaranteed by finding a bounded domain DM on functions f and g. Then, sufficient conditions for the existence of monotone solution to the problem are established by applying monotone iteration method. Moreover, two efficient iterative schemes are proposed, and the convergence of the iterative process is proved by using the monotonicity assumption on f and g. In particular, a new algorithm which combines Gauss-Kronrod quadrature method with cubic spline interpolation method is adopted to achieve the monotone iteration method in Matlab environment, and the high-precision approximate solution is obtained. Finally, the main results of the paper are illustrated by some numerical simulations, and the approximate solutions graphs are provided by using the iterative method. [ABSTRACT FROM AUTHOR]

The role of Riccati type systems in the plane along with the re-lated linear, second order differential equation is examined. If x and y are the variables of the Riccati differential equation, then any integrable Riccati system has two independent invariant curves dependent upon these variables whose nature is easily determined from the solution of the linear equation. Each of these curves has the same cofactor. Other invariant curves depend upon x alone and are shown to be less important. The systems have both Liouvillian and non{Liouvillian solutions and are easily transformable to sym-metric systems. However, systems derived from them may not be symmetric in their transformed variables. Several systems from the literature are discussed with regard to the forms of the invariant curves presented in the paper. The relation of certain Riccati type systems is considered with respect to Abel differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we focus on stability analysis of steady-state solutions of a predator-prey system with hunting cooperation functional response. The results show that the Turing instability can be a ected not only the existence of hunting cooperation, but also the di usion coefficients: (1) in the absence of predator diffusion, diffusion-driven instability can be induced by hunting cooperation, but no stable patterns appear; (2) the system can occur diffusion-driven instability and Turing patterns, when both predator and prey have diffusion, and the diffusion coefficient of prey is greater than that of the predator. The numerical simulations of two cases are presented to verify the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion. [ABSTRACT FROM AUTHOR]

This paper is concerned about exponential stability in mean square of Markovian switching delayed reaction-diffusion neutral-type stochastic neural networks (RNSNNs). By Lyapunov function method, several novel stability criteria on exponential mean square stability of Markovian switching RNSNNs with time-varying delays are obtained. In the end, two examples are given to verify the feasibility of our findings. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of third-order neutral impulsive differential equations. An equivalent class of neutral differential equations is obtained by using a suitable substitution. Some new oscillation results are proved. Moreover, we discuss the asymptotic behavior of the solution. The results presented here are illustrated via examples. [ABSTRACT FROM AUTHOR]

Considering the individual difference, this paper deals with an infection-age structured epidemic model coupling within-host and between-host for environmentally-driven infectious disease. The full system with two time scales, the cellular level and population level, is first separated into the isolated fast and slow systems. For the isolated fast and slow systems, com-bined with the within-host and between-host reproduction numbers, Rw0 and Rb0, we give the complete global dynamics by using Lyapunov function re-spectively. Our results indicate that when there is no virus in environment the disease can be not only controlled, but also eliminated. However, when there is always virus in environment the disease is only controlled but not e-liminated. Furthermore, the coupled slow system has complex dynamics with multiple positive equilibria and backward bifurcation. The virus contaminated environment plays a critical role on backward bifurcation. When the initial environmental virus is below some threshold the disease will be eliminated, when it is above the threshold the disease will develop an endemic disease. Some numerical simulations are performed to illustrate these results. The age structured model is more general, and this work includes some previous results. [ABSTRACT FROM AUTHOR]

In this paper, by using the Krasnoselskii's fixed-point theorem, we study the existence of positive periodic solutions of the following single-species model with delay weak kernel and cycle mortality:... and get the necessary conditions for the existence of positive periodic solutions. Finally, an example and numerical simulation are used to illustrate the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence and uniqueness of solution's to time-varying delays stochastic fractional differential equations (SFDEs) with non-Lipschitz coeffcients. By using fractional calculus and stochastic analysis, we can obtain the existence result of solutions for stochastic fractional differential equations. [ABSTRACT FROM AUTHOR]

By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree n. We obtain that the upper bound is 7[(n - 3)/2] + 5 when n = 5, 8 when n = 4, 5 when n = 3, 4 when n = 2, and 0 when n = 1 or n = 0, which linearly depends on n. [ABSTRACT FROM AUTHOR]

The Hopf cyclicities of some smooth polynomial, rational poly-nomial and piecewise smooth Liénard systems are studied. For two Liénard systems with the same damping term and different restoring (or potential) terms, we provide sufficient conditions that the two systems have the same Hopf cyclicity. Then, some examples are given to illustrate the efficiency and applicability of our results. [ABSTRACT FROM AUTHOR]

A singularly perturbed boundary value problem with weak nonlinearity in the case when the degenerate equation has a multiple root is studied. The asymptotic approximation of the solution is constructed by the modified boundary layer function method. Based on the comparison principle, there exist multizonal boundary layers in the neighborhood of the endpoints. The existence of a solution is proved by using the method of asymptotic differential inequalities. [ABSTRACT FROM AUTHOR]