Existence of periodic solutions for a periodic mutualism model on time scales

By using Mawhin's continuation theorem of coincidence degree theory, sufficient criteria are obtained for the existence of periodic solutions of the mutualism model

     

Positive periodic solutions of a periodic survival red blood cell model

By using the continuation theorem of coincidence degree theory by Gaines and Mawhin, a sufficient and realistic condition is obtained for the existence of a periodic survival red blood cell model.     

Positive almost periodic solutions for a delay logarithmic population model

By utilizing the continuation theorem of coincidence degree theory, we shall prove that a delay logarithmic population model has at least one positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result.     

Almost periodic solutions for some integrodifferential equations with infinite delay

By using a Liapunov functional, the conditions of existence and uniqueness of almost periodic solutions for some integrodifferential equations are obtained.     

Positive solutions for nonlinear periodic problems

We consider a nonlinear periodic problem driven by the scalar p-Laplacian and with a nonsmooth potential. Using the degree map for multivalued perturbations of (S)₊-operators and the spectrum of a weighted eigenvalue problem for the scalar periodic p-Laplacian, we prove the existence of a strictly positive solution. Michael E. Filippakis: Researcher supported by a grant of the National Scholarship Foundation of Greece (I.K.Y.)     

Construction of periodic solutions of integrodifferential equations of viscoelasticity

A theorem on the estimation of the periodic solutions of a linear integrodifferential equation and a theorem of existence and uniqueness of the periodic solution of a nonlinear integrodifferential equation are presented without proof.     

Nonlinear integrodifferential equations anda priori bounds on periodic solutions

Summary This paper studies the existence of aperiodic solution of a nonlinear integrodifferential system of the form , for each continuous periodic function p and under suitable assumptions on f, k and g. A topological transversality method is employed to obtain the existence of periodic solutions. This method relies ona priori bounds on periodic solutions. Several examples are provided where a variant of Liapunov's direct method is employed to obtaina priori bounds on periodic solutions.     

Existence of asymptotically almost periodic solutions for some second-order hyperbolic integrodifferential equations

Semigroup Forum - In this paper we study and obtain the existence of asymptotically almost periodic solutions to some classes of second-order hyperbolic integrodifferential equations of...     

Unique existence of periodic solutions of neutral Volterra integrodifferential equations

This paper deals with the uniqueness and existence of periodic solutions of neutral Volterra integrodifferential equations (1) and (2). Some new unique existence criteria are obtained.The project is supported by the National Natural Science Foundation of China.     

Positive periodic solutions for impulsive predator-prey model with dispersion and time delays

In this paper, we study the existence and global attractivity of positive periodic solutions for impulsive predator-prey systems with dispersion and time delays. By using coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions, and by means of a suitable Lyapunov functional, the uniqueness and global attractivity of positive periodic solution is presented. Some known results subject to the underlying systems without impulses are improved and generalized.     

Positive pseudo almost periodic solutions for a delayed differential neoclassical growth model

This paper is concerned with a non-autonomous delayed differential neoclassical growth model with an oscillating death rate. Under proper conditions, we employ a novel argument to establish a criterion on the existence and global exponential stability of positive pseudo almost periodic solution, which improves and extends some known relevant results. Finally, we present an example along with its numerical simulations to demonstrate the validity of the proposed result.     

Finding the initial values of periodic solutions of certain integrodifferential equations

A constructive method is proposed for approximately finding the initial values of periodic solutions of linear integrodifferential equations of Volterra type. The solvability of a system of determining equations is established.. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 944–951, July, 1990.     

Construction of periodic solutions of second-order differential and integrodifferential wave equations

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 1, pp. 48–53, January–February, 1988.     

Positive periodic solutions for impulsive Gause-type predator-prey systems

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.     

Positive almost periodic solutions for recurrent neural networks

In this paper recurrent neural networks with time-varying delays and continuously distributed delays are considered. Sufficient conditions for the existence and exponential stability of the positive almost periodic solutions are established, which are new and complement previously known results.     

非线性微分方程的正周期解

§ 1　 IntroductionIn[1 ] ,Saker and Agarwal studied the existence and uniqueness of positive periodicsolutions of the nonlinear differential equationN′(t) =-δ(t) N(t) + p(t) N(t) e- a N(t) ,(1 )whereδ(t) and p(t) are positive T-periodic functions.They proved that if p* >δ* ,then(1 ) has a unique T-periodic positive solution,wherep* =min0≤ t≤ Tp(t) ,δ* =max0≤ t≤ Tδ(t) .　　In view ofthe papermentioned above,whatcan be said aboutequation(1 ) when p* ≤δ* ?In this paper,we conside…     

Positive periodic solutions of second-order differential equations

In this work, we have obtained existence results for single and multiple positive periodic solutions for a class of second-order differential equations. Our results are based on a fixed point theorem for cones.