In this paper, a food chain model with Holling type II functional response on time scales is investigated. By using the Mawhin’s continuation theorem in coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Keywords—Periodic solutions; food chain model; coincidence degree; time scales.

In this paper, by applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result. Keywords—Almost periodic solution; Multi-d...

This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established. Keywords—Coincidence degree, continuation theorem, periodic solutions, time scales

In the present paper, we introduce some singular integral operators, singular quadrature operators and discretization matrices of singular integral equations with Hilbert kernel. These results both improve the classical theory of singular integral equations and develop the theory of singular quadrature with Hilbert kernel. Then by using them a unified framework for various collocation methods o...

By using Mawhin’s continuation theorem of coincidence degree theory, we establish the existence of 2 positive periodic solutions for n species non-autonomous Lotka-Volterra competition systems with harvesting terms. An example is given to illustrate the effectiveness of our results. Keywords—Positive periodic solutions; Lotka-Volterra competition system; Coincidence degree; Harvesting term.

In 1973 William Lawvere published a paper (reprinted as (Lawvere 2002)) where he explained that partial orders and metric spaces are examples of categories enriched in a closed category. Indeed, preorders are categories enriched over the two-element Boolean algebra 2, while (generalized) metric spaces are categories enriched over ([0,∞],+). Lawvere’s idea has been extremely influential in the f...

In this paper, we obtain several new generalized KKM-type theorems under a new coercivity condition and the condition of intersectionally closedness which improves condition of transfer closedness. As applications, we obtain new versions of equilibrium problem, minimax inequality, coincidence theorem, fixed point theorem and an existence theorem for an 1-person game.

It is of main interest in the theory of Fourier series the reconstruction of a function from the partial sums of its Fourier series. Just to mention two examples: Billard proved [2] the theorem of Carleson for the Walsh-Paley system, that is, for each function in L we have the almost everywhere convergence Snf → f and Fine proved [4] the Fejér-Lebesgue theorem, that is for each integrable funct...

Coupled coincidence and fixed point problems have been in the focus of the research interest for last few years. The problem was introduced in fuzzy metric spaces only recently in 2011. In this paper we work out a coupled coincidence point theorem for a compatible pair of mappings in fuzzy metric spaces. The space endowed with a partial ordering. We use a combination of analytic and order theor...

One can view a 2-parameter Brownian sheet {W (s, t); s, t ≥ 0} as a stream of interacting Brownian motions {W (s, •); s ≥ 0}. Given this viewpoint, we aim to continue the analysis of Walsh (1978) on the local times of the stream W (s, •), near time s = 0. Our main result is a kind of maximal inequality that, in particular, verifies the following conjecture of Khoshnevisan (1995a): as s → 0, the...