Abstract In this paper, we study the existence and uniqueness of a periodic solution for third-order neutral delay differential equation (NDDE) by applying Mawhin’s continuation theorem coincidence degree analysis techniques. An illustrative example is given as an application to support our results. To confirm accuracy results, also present plot behavior solution.

Von Neumann proved the minimax theorem (existence of a saddle-point solution to 2 person, zero sum games) in 1928. While his second article on the minimax theorem, stating the proof, has long been translated from German, his first announcement of his result (communicated in French to the Academy of Sciences in Paris by Borel, who had posed the problem settled by Von Neumann’s proof) is translat...

We study the existence of periodic solutions for a nonlinear system of n-th order di erential equations on time-scales. Assuming a suitable Nirenberg type condition, we prove the existence of at least one solution of the problem using Mawhin's coincidence degree.

We utilize a condition for algebraic curvature operators called surgery stability as suggested by the work of Hoelzel to investigate space riemannian metrics over closed manifolds satisfying these conditions. Our main result is parametrized Gromov–Lawson construction with not necessarily trivial normal bundles and shows that homotopy type this invariant under surgeries suitable codimension. Thi...

Sufficient conditions for the uniform convergence of polynomials Pniz) of best qth power approximation to a given function /(z) of a complex variable on a smooth curve Y were presented in an early paper by Jackson [1]. Although his theorem has found frequent application in approximation theory (see [2]), only slight extensions of the result are to be found in the literature. The present paper g...

We establish a maximin characterisation of the linear escape rate of the orbits of a non-expansive mapping on a complete (hemi-)metric space, under a mild form of Busemann’s non-positive curvature condition (we require a distinguished family of geodesics with a common origin to satisfy a convexity inequality). This characterisation, which involves horofunctions, generalises the Collatz-Wielandt...

By means of Mawhin’s continuation theorem of coincidence degree theory, some new sufficient conditions are obtained for the existence of at least four positive almost periodic solutions for a harvesting mutualism model with time delays. To the best of the author’s knowledge, so far, the result of this paper is completely new. An example is employed to illustrate the result of this paper.

A periodic discrete time three species competition system is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous nonautonomous three species competition system is proposed. By using Gaines andMawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive periodic solutions of t...

With the help of the coincidence degree and the related continuation theorem, we explore the existence of at least two periodic solutions of a delayed ratio-dependent predator-prey system with exploited term. Some easily verifiable sufficient criteria are established for the existence of at least two positive periodic solutions.

A delayed periodic n-species simple food-chain system with Holling type-II functional response is investigated. By means of Gaines and Mawhin’s continuation theorem of coincidence degree theory and by constructing appropriate Lyapunov functionals, sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the system.