Single-period Two-product Inventory Model with Reorder and Substitution

In market, excess demands for many products can be met by reorder even during one period, and retailers usually adopt substitution strategy for more benefit. Under the retailer's substitution strategy and permission of reorder, we develop the profits maximization model for the two-substitutable-product inventory problem with stochastic demands and proportional costs and revenues. We show that the objective function is concave and submodular, and therefore the optimal policy exists. We present the optimal conditions for order quantity and provide some properties of the optimal order quantities. Comparing our model with Netessine and Rudi's, we prove that reorder and adoption of the substitution strategy can raise the general profits and adjust down the general stock level.     

Existence of Single and Multiple PositivePeriodic Solutions for a Kindof Delay Logistic Equations

W匕eonsider the existenee of single and multiple positive periodie solutions for the generalperiodie Logistie equation ,‘(t)=夕(t)!a(t)一f(t,夕(t一几(t)),…,夕(t一几,(t)))],t‘R,(E)wheref:Rx皿+’‘什矿15 eontinuous,a(t)〔C(皿,R+),瑞(亡)〔C(R,R),anda(t)=a(t+T),几二(t)=爪(t+T),饥=1,…,,z,f(t,。1,。2,…,。,,)=f(亡+T,。,,。2,…,。。),T>O· It 15 well known that many matliematieal eeologieal Logistie equations are related to tl、eequation(E),e.g.,(1)the single speeies periodie populatio,i ,,…     

Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems

This paper is devoted to the study ofthe existence of single and multiple positive solutions forthe first order boundary value problem x′= f(t,x),x(0)=x(T),where f ∈ C([0,T]×R).In addition,weapply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at theorigin.Our proofs are based on a fixed point theorem in cones.Our results improve some recent results in theliteratures.     

Positive Periodic Solutions of a Class of Non-autonomous Single Species Population Model with Delays and Feedback Control

With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.     

Generalizing the Keller�CSegel Model: Lyapunov Functionals, Steady State Analysis, and Blow-Up Results for Multi-species Chemotaxis Models in?the?Presence of Attraction and Repulsion Between Competitive Interacting Species

In this paper we extend the famous Keller–Segel model for the chemotactic movement of motile species to some multi-species chemotaxis equations. The presented multi-species chemotaxis models are more general than those introduced so far and also include some interaction effects that have not been studied before. For example, we consider multi-species chemotaxis models with attraction and repulsion between interacting motile species. For some of the presented new models we give sufficient conditions for the existence of Lyapunov functionals. These new results are related to those of Wolansky (Scent and sensitivity: equilibria and stability of chemotactic systems in the absence of conflicts, preprint, 1998; Eur. J. Appl. Math. 13:641–661, 2002). Furthermore, a linear stability analysis is performed for uniform steady states, and results for the corresponding steady state problems are established. These include existence and nonexistence results for non-constant steady state solutions in some special cases.