Periodic solutions to a generalized Basener-Ross model with time-dependent coefficients

This paper is devoted to studying the existence of at least one periodic solution for a generalized Basener-Ross model with time-dependent coefficients. The discussion is based on the Man\’asevich-Mawhin continuation theorem and fixed point theorem of cone mapping together with some properties of Green’s function.

New result of existence of periodic solutions for a generalized p-Laplacian Liénard type differential equation with a variable delay

In this paper, we propose a generalized [Formula: see text]-Laplacian Liénard type differential equation with a variable delay. By applying the Mawhin continuation theorem, we established a set of sufficient conditions on the existence of at least one periodic solution with period [Formula: see text]. It is significant that the growth degree with respect to the variables [Formula: see text] imposed on [Formula: see text] is allowed to be greater than [Formula: see text] and the growth degree with respect to the variables [Formula: see text] imposed on [Formula: see text] is allowed to be greater than [Formula: see text] so the result not only improves but also generalizes. Some examples are provided to illustrate the results.

Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance

We investigate a (k,n-k) conjugate boundary value problem with integral boundary conditions. By using Mawhin continuation theorem, we study the solvability of this boundary value problem at resonance. It is shown that the boundary value problem (-1)n-kφ(n)(x)=fx,φx,φ′x,…,φ(n-1)(x), x∈[0,1], φ(i)(0)=φ(j)(1)=0, 1≤i≤k-1, 0≤j≤n-k-1, φ(0)=∫01φ(x)dA(x) has at least one solution under some suitable conditions.

Some Results for Periodic Solutions of a Kind of Liénard Equation

We investigate the following Liénard-typep-Laplacian equation with a deviating argument(φp(x′t))′+f(xt)x′t+βtgxt-τt=e(t). Some new criteria for guaranteeing the existence and uniqueness of periodic solutions of this equation are given by using the Manásevich-Mawhin continuation theorem and some analysis techniques. Our results hold under weaker conditions than some known results from the literature and are more effective. In the last section, an illustrative example is provided to demonstrate the applications of the theoretical results.

2 N POSITIVE PERIODIC SOLUTIONS TO N SPECIES NON‐AUTONOMOUS LOTKA‐VOLTERRA UNIDIRECTIONAL FOOD CHAINS WITH HARVESTING TERMS

By using the Mawhin continuation theorem of coincidence degree theory and some results on inequalities, we establish the existence of 2 n positive periodic solutions for n species non‐autonomous Lotka‐Volterra unidirectional food chains with harvesting terms. Two examples are given to illustrate the effectiveness of our results.

A NOTE ON PERIODIC SOLUTIONS OF A FORCED LIÉNARD-TYPE EQUATION

Criteria for guaranteeing the existence, uniqueness and asymptotic stability (in the sense of Liapunov) of periodic solutions of a forced Liénard-type equation under certain assumptions are presented. These criteria are obtained by application of the Manásevich–Mawhin continuation theorem, Floquet theory, Liapunov stability theory and some analysis techniques. An example is provided to demonstrate the applicability of our results.

EXISTENCE AND STABILITY OF PERIODIC SOLUTIONS OF A RAYLEIGH TYPE EQUATION

In this work, we shall be concerned with the following forced Rayleigh type equation: Under certain assumptions, some criteria for guaranteeing the existence, uniqueness and asymptotic stability (in the Lyapunov sense) of periodic solutions of this equation are presented by applying the Manásevich–Mawhin continuation theorem, Floquet theory, Lyapunov stability theory and some analysis techniques. Moreover, an example is provided to demonstrate the applications of our results.