Mathematics open access research

Optimal harvesting control and dynamics of two-species stochastic model with delays
30 citations*

Taking the stochastic effects on growth rate and harvesting effort into account, we propose a stochastic delay model of species in two habitats. The main aim of this paper is to investigate optimal harvesting and dynamics of the stochastic delay model. By using the stochastic analysis theory and differential inequality technology, we firstly obtain sufficient conditions for persistence in the mean and extinction. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are gained by using Hessian matrix, the ergodic method, and optimal harvesting theory of differential equations. To illustrate the performance of the theoretical results, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients.

Lidan Liu and Xinzhu Meng

Nadler’s fixed point theorem in v-generalized metric spaces
3 citations*

We extend Nadler’s fixed point theorem to ν-generalized metric spaces. Through the proof of the above extension, we understand more deeply the mathematical structure of a ν-generalized metric space. In particular, we study the completeness of the space. We also improve Caristi’s and Subrahmanyam’s fixed point theorems in the space.

Tomonari Suzuki

Fourier series of higher-order Bernoulli functions and their applications
17 citations*

In this paper, we study the Fourier series related to higher-order Bernoulli functions and give new identities for higher-order Bernoulli functions which are derived from the Fourier series of them.

Taekyun Kim, Dae San Kim, Seog-Hoon Rim, and Dmitry V. Dolgy

Positive solutions to boundary value problems of p-Laplacian with fractional derivative
26 citations*

Based on a variational approach, we prove that a second-order singular damped differential equation has at least one periodic solution when some reasonable assumptions are satisfied.

Xiaoyu Dong, Zhanbing Bai, and Shuqin Zhang