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In this paper, we are concerned about a predator–prey model with Beddington–DeAngelis functional response, in which a protection zone is set for the prey. In a previous paper, it has been shown that the coefficient k measuring the mutual interference between predators in the Beddington–DeAngelis functional response plays a crucial role in the predator–prey system. As k is large enough, there exists a unique globally stable positive stationary solution except a special case. By introducing an equivalent system, this paper reveals that the uniqueness and global stability still holds true in the special case. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of traveling waves for a nonlocal dispersal Kermack–McKendrick epidemic model. As we know, due to the semiflow generated by the model does not have the order-preserving property and the solutions lack of regularity, it is difficult to investigate traveling waves with the critical wave speed. Furthermore, the nonlocal dispersal and bilinear incidence bring additional difficulties to get the boundedness of traveling waves. In the present paper, we overcome these difficulties to obtain the boundedness of traveling waves by analysis technique firstly and then prove the existence of traveling waves under the critical wave speed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the nonlocal diffusive model with double free boundaries in spatial heterogeneous environment, where the spatial heterogeneity is described by the sign indefinite coefficients. Such a model can be used to illustrate the spreading or vanishing of a new or invasive species. Due to the lack of comparison principle in the nonlocal reaction–diffusion equation, many classical methods cannot be used directly to this nonlocal problem. This motivates us to find new techniques. We first establish the spreading–vanishing dichotomy as well as some criteria that ensure the species spreading or vanishing by principal eigenvalues of associated scalar elliptic eigenvalue problems. And then we determine the spreading speed when spreading occurs. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the spreading speeds and traveling wavefronts for second order integrodifference equations. By introducing an auxiliary integrodifference system, the spreading speed is established for the integrodifference equation. It is shown that the spreading speed coincides with the minimal wave speed for monotonic traveling wavefronts. Furthermore, we prove that the traveling wavefronts are stable by applying the squeezing technique. Finally, we analyze the different effects of the delay term appearing in the integrodifference equation from the viewpoint of ecology. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the asymptotic stability of traveling wave fronts of a class of nonlocal reaction–diffusion equations with delay. Under monostable assumption, we prove that the traveling wave front is exponentially stable by means of the (technical) weighted energy method, when the initial perturbation around the wave is suitable small in a weighted norm. The exponential convergent rate is also obtained. Finally, we apply our results to some population models and obtain some new results, which recover, complement and/or improve a number of existing ones. [Copyright &y& Elsevier]

Abstract: In this paper we study the existence and multiplicity of the solutions for the fourth-order boundary value problem (BVP) , , , where is continuous, and are parameters. By means of the idea of the decomposition of operators shown by Chen [W.Y. Chen, A decomposition problem for operators, Xuebao of Dongbei Renmin University 1 (1957) 95–98], see also [M. Krasnosel''skii, Topological Methods in the Theory of Nonlinear Integral Equations, Gostehizdat, Moscow, 1956], and the critical point theory, we obtain that if the pair is on the curve satisfying , then the above BVP has at least one, two, three, and infinitely many solutions for λ being in different interval, respectively. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the existence and global stability of the positive periodic solutions of delayed discrete food chains with omnivory. With the help of continuation theorem in coincidence degree theory and Lyapunov functions, some sufficient conditions are obtained. The results show that, for such a system with omnivory, more conditions are required for the persistence of the positive periodic solutions than that of a linear food chain. On the other hand, omnivory makes no differences on the stability of the solutions. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence and nonexistence of positive solutions of the second-order nonlinear dynamic equation , , satisfying either the conjugate boundary conditions or the right focal boundary conditions , where a and f are positive. We show that there exists a such that the above boundary value problem has at least two, one and no positive solutions for , and , respectively. Furthermore, by using the semiorder method on cones of the Banach space, we establish an existence and uniqueness criterion for positive solution of the problem. In particular, such a positive solution of the problem depends continuously on the parameter λ, i.e., is nondecreasing in λ, and . [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence and nonexistence of positive solutions of the nonlinear fourth-order beam equation , , , where is continuous and ζ, η and λ are parameters. We show that there exists a such that the above boundary value problem (BVP) has at least two, one and no positive solutions for , and , respectively. Furthermore, by using the semiorder method on cones of Banach space, we establish a uniqueness criterion for positive solution of the BVP. In particular such a positive solution of the BVP depends continuously on the parameter λ, i.e., is nondecreasing in λ, and for any . [Copyright &y& Elsevier]

Abstract: In this paper, the existence of solution on a compact interval to second order impulsive functional differential inclusions is investigated. Several new results are obtained by using suitable fixed point theorem. [Copyright &y& Elsevier]

Abstract: Let be a time scale such that . Consider the following three-point boundary value problem on time scales: where , , , , and . By using fixed point theorems in cones, some new and general results are obtained for the existence of single and multiple positive solutions of the above problem. In particular, our criteria generalize and improve some known results. [Copyright &y& Elsevier]

Abstract: Sufficient conditions are established for the permanence in a delayed discrete predator–prey model with Holling type III functional response: Our investigation confirms that when the death rate of the predator is rather small as well as the intrinsic growth rate of the prey is relatively large, the species could coexist in the long run. [Copyright &y& Elsevier]

Classification schemes for positive solutions of a class of second order nonlinear differential systems are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also provided. [Copyright &y& Elsevier]

In this paper we consider the existence and uniqueness of positive periodic solution for the periodic equation y′(t)=−a(t)y(t)+λh(t)f(y(t−τ(t))). By the eigenvalue problems of completely continuous operators and theory of α-concave or −α-convex operators and its eigenvalue, we establish some criteria for existence and uniqueness of positive periodic solution of above functional differential equations with parameter. In particular, the unique solution yλ(t) of the above equation depends continuously on the parameter λ. Finally, as an application, we obtain sufficient condition for the existence of positive periodic solutions of the Nicholson blowflies model. [Copyright &y& Elsevier]

In this paper, existence criteria for three positive solutions of the nonlinear three-point boundary value problem u″(t)+a(t)u′(t)+b(t)u(t)+h(t)f(u)=0, t∈(0,1),u(0)=0, u(1)=αu(η), are established by using the Leggett–Williams fixed point theorem. An example is also included to illustrate the importance of the result obtained. [Copyright &y& Elsevier]

In this paper, we investigate optimal policies for an age-dependent n-dimensional food chain model, which is controlled by fertility. By using Dubovitskii–Milyutin''s general theory, the maximum principles are obtained for problems with free terminal states, infinite horizon and target sets, respectively. [Copyright &y& Elsevier]