On periodic solutions of a discrete Nicholson’s dual system with density-dependent mortality and harvesting terms

In this study, we discuss the existence of positive periodic solutions of a class of discrete density-dependent mortal Nicholson’s dual system with harvesting terms. By means of the continuation coincidence degree theorem, a set of sufficient conditions, which ensure that there exists at least one positive periodic solution, are established. A numerical example with graphical simulation of the model is provided to examine the validity of the main results.

THE EXISTENCE OF POSITIVE PERIODIC SOLUTIONS OF AN ECO-EPIDEMIC MODEL WITH IMPULSIVE BIRTH

In this paper, we considered an eco-epidemic model with impulsive birth. By using the coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions.

Existence and Global Exponential Stability of Periodic Solutions for General Neural Networks with Time-Varying Delays

By using the coincidence degree theorem and differential inequality techniques, sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general neural networks with time-varying (including bounded and unbounded) delays. Some known results are improved and some new results are obtained. An example is employed to illustrate our feasible results.

A symmetric solution of a multipoint boundary value problem at resonance

We apply a coincidence degree theorem of Mawhin to show the existence of at least one symmetric solution of the nonlinear second-order multipoint boundary value problemu″(t)=f(t,u(t),|u′(t)|),t∈(0,1),u(0)=∑i=1nμiu(ξi),u(1−t)=u(t),t∈[0,1], where0<ξ1<ξ2<…<ξn≤1/2,∑i=1nμi=1,f:[0,1]×ℝ2→ℝwithf(t,x,y)=f(1−t,x,y),(t,x,y)∈[0,1]×ℝ2, satisfying the Carathéodory conditions.