Nonlinear Analysis: Modelling and Control

Journal Information
ISSN / EISSN : 1392-5113 / 1392-5113
Published by: Vilnius University Press (10.15388)
Total articles ≅ 848
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Latest articles in this journal

Sergey Smirnov
Nonlinear Analysis: Modelling and Control, Volume 26, pp 914-927; https://doi.org/10.15388/namc.2021.26.23932

Abstract:
The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.
Nonlinear Analysis: Modelling and Control, Volume 26, pp 969-991; https://doi.org/10.15388/namc.2021.26.24299

Abstract:
In this study, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the one-dimensional Sturm–Liouville equation with one classical-type Dirichlet boundary condition and integral-type nonlocal boundary condition. We investigate solutions of special initial value problem and find asymptotic formulas of arbitrary order. We analyze the characteristic equation of the boundary value problem for eigenvalues and derive asymptotic formulas of arbitrary order. We apply the obtained results to the problem with integral-type nonlocal boundary condition.
Yang Yang, Xinzhi Wang,
Nonlinear Analysis: Modelling and Control, Volume 26, pp 801-820; https://doi.org/10.15388/namc.2021.26.23963

Abstract:
This paper considers a delayed claim risk model with stochastic return and Brownian perturbation in which each main claim may be accompanied with a delayed claim occurring after a stochastic period of time, and the price process of the investment portfolio is described as a geometric Lévy process. By means of the asymptotic results for randomly weighted sum of dependent subexponential random variables we obtain some asymptotics for finite-time ruin probability. A simulation study is also performed to check the accuracy of the obtained theoretical result via the crude Monte Carlo method.
Nonlinear Analysis: Modelling and Control, Volume 26, pp 759-780; https://doi.org/10.15388/namc.2021.26.23935

Abstract:
This article aims to study a class of discontinuous fuzzy inertial Cohen–Grossberg neural networks (DFICGNNs) with discrete and distributed time-delays. First of all, in order to deal with the discontinuities by the differential inclusion theory, based on a generalized variable transformation including two tunable variables, the mixed time-varying delayed DFICGNN is transformed into a first-order differential system. Then, by constructing a modified Lyapunov–Krasovskii functional concerning with the mixed time-varying delays and designing a delayed feedback control law, delay-dependent criteria formulated by algebraic inequalities are derived for guaranteeing the finite-time stabilization (FTS) for the addressed system. Moreover, the settling time is estimated. Some related stability results on inertial neural networks is extended. Finally, two numerical examples are carried out to verify the effectiveness of the established results.
, Nikolajus Kozulinas,
Nonlinear Analysis: Modelling and Control, Volume 26, pp 947-968; https://doi.org/10.15388/namc.2021.26.24502

Abstract:
The nonstationary Navier–Stokes equations are studied in the infinite cylinder Π = {x = (x', xn) ∈ Rn: x' ∈ σ ∈ R n – 1: – ∞ < xn < ∞, n = 2, 3} under the additional condition of the prescribed time-periodic flow-rate (flux) F(t). It is assumed that the flow-rate F belongs to the space L2(0, 2π), only. The time-periodic Poiseuille solution has the form u(x, t) = (0, ... , 0, U(x', t)), p(x,t) = –q(t)xn + p0(t), where (U(x', t), q(t)) is a solution of an inverse problem for the time-periodic heat equation with a specific over-determination condition. The existence and uniqueness of a solution to this problem is proved.
Nonlinear Analysis: Modelling and Control, Volume 26, pp 781-800; https://doi.org/10.15388/namc.2021.26.21945

Abstract:
In this paper, we establish some point of φ-coincidence and common φ-fixed point results for two self-mappings defined on a metric space via extended CG-simulation functions. By giving an example we show that the obtained results are a proper extension of several well-known results in the existing literature. As applications of our results, we deduce some results in partial metric spaces besides proving an existence and uniqueness result on the solution of system of integral equations.
Nonlinear Analysis: Modelling and Control, Volume 26, pp 884-913; https://doi.org/10.15388/namc.2021.26.24441

Abstract:
Prostate cancer represents the second most common cancer diagnosed in men and the fifth most common cause of death from cancer worldwide. In this paper, we consider a nonlinear mathematical model exploring the role of neuroendocrine transdifferentiation in human prostate cancer cell dynamics. Sufficient conditions are given for both the biological relevance of the model’s solutions and for the existence of its equilibria. By means of a suitable Liapunov functional the global asymptotic stability of the tumour-free equilibrium is proven, and through the use of sensitivity and bifurcation analyses we identify the parameters responsible for the occurrence of Hopf and saddle-node bifurcations. Numerical simulations are provided highlighting the behaviour discovered, and the results are discussed together with possible improvements to the model.
, , Mei Wei
Nonlinear Analysis: Modelling and Control, Volume 26, pp 928-946; https://doi.org/10.15388/namc.2021.26.24176

Abstract:
In this paper, we discuss the asymptotically periodic problem for the abstract fractional evolution equation under order conditions and growth conditions. Without assuming the existence of upper and lower solutions, some new results on the existence of the positive S-asymptotically ω-periodic mild solutions are obtained by using monotone iterative method and fixed point theorem. It is worth noting that Lipschitz condition is no longer needed, which makes our results more widely applicable.
Hiromi Seno
Nonlinear Analysis: Modelling and Control, Volume 26, pp 861-883; https://doi.org/10.15388/namc.2021.26.24177

Abstract:
As the number of internet users appears to steadily increase each year, Internet Gaming Disorder (IGD) is bound to increase as well. The question how this increase will take place, and what factors have the largest impact on this increase, naturally arises. We consider a system of ordinary differential equations as a simple mathematical model of the population dynamics about the internet gaming. We assume three stages about the internet gamer’s state: moderate, addictive, and under treatment. The transition of the gamer’s state between the moderate and the addictive stages is significantly affected by the social nature of internet gaming. As the activity of social interaction gets higher, the gamer would be more likely to become addictive. With the inherent social reinforcement of internet game, the addictive gamer would hardly recontrol his/herself to recover to the moderate gamer. Our result on the model demonstrates the importance of earlier initiation of a system to check the IGD and lead to some medical/therapeutic treatment. Otherwise, the number of addictive gamers would become larger beyond the socially controllable level.
Maryam Ramezani, ,
Nonlinear Analysis: Modelling and Control, Volume 26, pp 821-841; https://doi.org/10.15388/namc.2021.26.24367

Abstract:
We present a novel generalization of the Hyers–Ulam–Rassias stability definition to study a generalized cubic set-valued mapping in normed spaces. In order to achieve our goals, we have applied a brand new fixed point alternative. Meanwhile, we have obtained a practicable example demonstrating the stability of a cubic mapping that is not defined as stable according to the previously applied methods and procedures.
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