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.

On the existence of almost periodic solutions of impulsive non-autonomous Lotka-Volterra predator-prey system with harvesting terms

<abstract><p>In this paper, by using the Mawhin's continuation theorem, some easily verifiable sufficient conditions are obtained to guarantee the existence of almost periodic solutions of impulsive non-autonomous Lotka-Volterra predator-prey system with harvesting terms. Our result corrects the result obtained in ^{[<xref ref-type="bibr" rid="b13">13</xref>]}. An example and some remarks are given to illustrate the advantage of this paper.</p></abstract>

Solutions to Neumann boundary value problems with a generalized 𝑝-Laplacian

The purpose of this work is to investigate the existence of solutions for various Neumann boundary value problems associated to the Laplacian-type operators. The main results are obtained using the extension of Mawhin’s continuation theorem.

Existence of Homoclinic Orbits for a Singular Differential Equation Involving p-Laplacian

The efficient conditions guaranteeing the existence of homoclinic solutions to second-order singular differential equation with p-Laplacian ϕpx′t′+fx′t+gxt+ht/1−xt=et are established in the paper. Here, ϕps=sp−2s,p>1,f,g,h,e∈Cℝ,ℝ with ht+T=ht. The approach is based on the continuation theorem for coincidence degree theory.

On the existence of periodic oscillations for pendulum-type equations

We provide new sufficient conditions for the existence of T-periodic solutions for the ϕ-laplacian pendulum equation (ϕ(x′))′ + k x′ + a sin x = e(t), where e ∈ C͠T. Our main tool is a continuation theorem due to Capietto, Mawhin and Zanolin and we improve or complement previous results in the literature obtained in the framework of the classical, the relativistic and the curvature pendulum equations.

Periodic solutions for second order differential equations with indefinite singularities

In this paper, the problem of periodic solutions is studied for second order differential equations with indefinite singularities $$\begin{array}{} \displaystyle x''(t)+ f(x(t))x'(t)+\varphi(t)x^m(t)-\frac{\alpha(t)}{x^\mu(t)}+\frac{\beta(t)}{x^y (t)}=0, \end{array}$$ where f ∈ C((0, +∞), ℝ) may have a singularity at the origin, the signs of φ and α are allowed to change, m is a non-negative constant, μ and y are positive constants. The approach is based on a continuation theorem of Manásevich and Mawhin with techniques of a priori estimates.

On some of convergence domains of multidimensional S-fractions with independent variables

The convergence of multidimensional S-fractions with independent variables is investigated using the multidimensional generalization of the classical Worpitzky's criterion of convergence, the criterion of convergence of the branched continued fractions with independent variables, whose partial quotients are of the form $\frac{q_{i(k)}^{i_k}q_{i(k-1)}^{i_k-1}(1-q_{i(k-1)})z_{i(k)}}{1}$, and the convergence continuation theorem to extend the convergence, already known for a small domain (open connected set), to a larger domain. It is shown that the union of the intersections of the parabolic and circular domains is the domain of convergence of the multidimensional S-fraction with independent variables, and that the union of parabolic domains is the domain of convergence of the branched continued fraction with independent variables, reciprocal to it.

Dynamics of two-species delayed competitive stage-structured model described by differential-difference equations

Overf the last few years, by utilizing Mawhin’s continuation theorem of coincidence degree theory and Lyapunov functional, many scholars have been concerned with the global asymptotical stability of positive periodic solutions for the non-linear ecosystems. In the real world, almost periodicity is usually more realistic and more general than periodicity, but there are scarcely any papers concerning the issue of the global asymptotical stability of positive almost periodic solutions of non-linear ecosystems. In this paper we consider a kind of delayed two-species competitive model with stage structure. By means of Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the existence of at least one positive almost periodic solutions for the above model with nonnegative coefficients. Furthermore, the global asymptotical stability of positive almost periodic solution of the model is also studied. The work of this paper extends and improves some results in recent years. An example and simulations are employed to illustrate the main results of this paper.

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.

Antiperiodic Solutions for Quaternion-Valued Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses

This paper is concerned with quaternion-valued shunting inhibitory cellular neural networks (QVSICNNs) with distributed delays and impulses. By using a new continuation theorem of the coincidence degree theory, the existence of antiperiodic solutions for QVSICNNs is obtained. By constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of antiperiodic solutions for QVSICNNs. Finally, an example is given to show the feasibility of obtained results.