Global positive periodic solutions of periodic n-species competition systems

AbstractIn this paper, an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of generalized n-species Lotka–Volterra type and Gilpin–Ayala type competition systems is obtained. It improves a series of the well-known sufficiency theorems in the literature about the problems mentioned above. The method is based on a well-known fixed point theorem in a cone of Banach space. This approach can be applied to more general competition systems

Necessary and sufficient conditions for oscillations of delay equations with impulses

AbstractIn this paper, a necessary and sufficient condition for oscillation of a first-order delay differential equation with impulses x′(t)+∑i=1npix(t−τi)=0, t≠tk,x(tk+)−x(tk=bkx(tk), k=1,2,… is established

Existence and uniqueness of positive solutions to three-point boundary value problems for second order impulsive differential equations

Using a fixed point theorem of generalized concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions to three-point boundary value problems for second order impulsive differential equations

Conditions for Oscillation of a Neutral Differential Equation

For a neutral differential equation with positive and changeable sign coefficients [x(t)−a(t)x(δ(t))]′+p(t)F(x(τ(t)))−q(t)G(x(σ(t)))=0, oscillation criteria are established, where q(t) is not required as nonnegative. Several new results are obtained

Strong oscillations for second order nonlinear functional differential equations

In this paper, we establish some strongly oscillation theorems for nonlinear second order functional differential equationx″(t)+p(t)f(x(t),x(g(t)))=0without assuming that g(t) is retarded or advanced

Existence of Multiple Positive Periodic Solutions of Delayed Predator-Prey Models with Functional Responses

AbstractIn this paper, by applying the continuation theorem of coincidence degree theory, we establish some new criteria for the existence of multiple positive periodic solutions for the delayed predator-prey model.x′(t)=x(t)(r(t)−a(t)x(t))−b(t)f(x(t))y(t),y′(t)=y(t)(c(t)f(x(t−τ))−d(t)),when functional response function f is monotonic or nonmonotonic

On existence of periodic solutions of the Rayleigh equation of retarded type

In this paper, we give two sufficient conditions on the existence of periodic solutions of the non-autonomous Rayleigh equation of retarded type by using the coincidence degree theory

Existence of Positive Periodic Solutions for n

In this paper we consider the existence, multiplicity, and nonexistence of positive periodic solutions for n-dimensional nonautonomous functional differential system x'(t)=H(t,x(t))-λB(t)F(x(t-τ(t))), where hi are ω-periodic in t and there exist ω-periodic functions αi,βi∈C(R,R+) such that αi(t)≤(hi(t,x)/xi)≤βi(t),∫0ω‍αi(t)dt>0, for x∈R+n all with xi>0, and t∈R, limxi→0+(hi(t,x)/xi) exist for t∈R; bi∈C(R,R+) are ω-periodic functions and ∫0ω‍bi(t)dt>0;fi∈C(R+n,R+), fi(x)>0 for x >0; τ∈(R,R) is an ω-periodic function. We show that the system has multiple or no positive ω-periodic solutions for sufficiently large or small λ>0, respectively