Nonlinear Analysis: Modelling and Control

Journal Information
ISSN / EISSN : 1392-5113 / 1392-5113
Current Publisher: Vilnius University Press (10.15388)
Total articles ≅ 348
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Latest articles in this journal

Wenwen Hou, , Ravi P. Agarwal, Guotao Wang
Nonlinear Analysis: Modelling and Control, Volume 26, pp 349-362; doi:10.15388/namc.2021.26.22358

Abstract:
This paper first introduces a generalized fractional p-Laplacian operator (–Δ)sF;p. By using the direct method of moving planes, with the help of two lemmas, namely decay at infinity and narrow region principle involving the generalized fractional p-Laplacian, we study the monotonicity and radial symmetry of positive solutions of a generalized fractional p-Laplacian equation with negative power. In addition, a similar conclusion is also given for a generalized Hénon-type nonlinear fractional p-Laplacian equation.
Venkatesan Nithya, ,
Nonlinear Analysis: Modelling and Control, Volume 26, pp 187-206; doi:10.15388/namc.2021.26.22355

Abstract:
The H∞ filtering problem for a class of networked nonlinear Markovian jump systems subject to randomly occurring distributed delays, nonlinearities, quantization effects, missing measurements and sensor saturation is investigated in this paper. The measurement missing phenomenon is characterized via a random variable obeying the Bernoulli stochastic distribution. Moreover, due to bandwidth limitations, the measurement output is quantized using a logarithmic quantizer and then transmitted to the filter. Further, the output measurements are affected by sensor saturation since the communication links between the system and the filter are unreliable and is described by sector nonlinearities. The objective of this work is to design a quantized resilient filter that guarantees not only the stochastic stability of the augmented filtering error system but also a prespecified level of H∞ performance. Sufficient conditions for the existence of desired filter are established with the aid of proper Lyapunov–Krasovskii functional and linear matrix inequality approach together with stochastic analysis theory. Finally, a numerical example is presented to validate the developed theoretical results.
Yunfeng Jia
Nonlinear Analysis: Modelling and Control, Volume 26, pp 293-314; doi:10.15388/namc.2021.26.22356

Abstract:
We introduce a reaction–diffusion system with modified nonlinear functional responses. We first discuss the large-time behavior of positive solutions for the system. And then, for the corresponding steady-state system, we are concerned with the priori estimate, the existence of the nonconstant positive solutions as well as the bifurcations emitting from the positive constant equilibrium solution. Finally, we present some numerical examples to test the theoretical and computational analysis results. Meanwhile, we depict the trajectory graphs and spatiotemporal patterns to simulate the dynamics for the system. The numerical computations and simulated graphs imply that the available food resource for consumer is very likely not single.
Lin Li, Donal O’Regan
Nonlinear Analysis: Modelling and Control, Volume 26, pp 227-240; doi:10.15388/namc.2021.26.20564

Abstract:
In this paper, we get the existence of two positive solutions for a fourth-order problem with Navier boundary condition. Our nonlinearity has a critical growth, and the method is a local minimum theorem obtained by Bonanno.
, Guotao Wang, Mei Wei
Nonlinear Analysis: Modelling and Control, Volume 26, pp 241-258; doi:10.15388/namc.2021.26.21656

Abstract:
This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of mild solutions for the abstract time-space evolution equation with delay under some quasimonotone conditions are obtained. Finally, the abstract results are applied to the time-space fractional delayed diffusion equation with fractional Laplacian operator, which improve and generalize the recent results of this issue.
Muhammad Usman Ali,
Nonlinear Analysis: Modelling and Control, Volume 26, pp 334-348; doi:10.15388/namc.2021.26.22357

Abstract:
In this article, we introduce fixed point theorems for multivalued mappings satisfying implicit-type contractive conditions based on a special form of simulation functions. We also provide an application of our result in integral inclusions. Our outcomes generalize/extend many existing fixed point results.
Rong Hu, , Yi-Bin Xiao
Nonlinear Analysis: Modelling and Control, Volume 26, pp 271-292; doi:10.15388/namc.2021.26.22429

Abstract:
Consider an abstract Problem P in a metric space (X; d) assumed to have a unique solution u. The aim of this paper is to compare two convergence results u'n → u and u''n → u, both in X, and to construct a relevant example of convergence result un → u such that the two convergences above represent particular cases of this third convergence. To this end, we use the concept of Tykhonov triple. We illustrate the use of this new and nonstandard mathematical tool in the particular case of hemivariational inequalities in reflexive Banach space. This allows us to obtain and to compare various convergence results for such inequalities. We also specify these convergences in the study of a mathematical model, which describes the contact of an elastic body with a foundation and provide the corresponding mechanical interpretations.
Marta Karaliutė, Kęstutis Dučinskas
Nonlinear Analysis: Modelling and Control, Volume 26, pp 363-374; doi:10.15388/namc.2021.26.22359

Abstract:
The novel approach to classification of spatio-temporal data based on Bayes discriminant functions is developed. We focus on the problem of supervised classifying of the spatiotemporal Gaussian random field (GRF) observation into one of two classes specified by different drift parameters, separable nonlinear covariance functions and nonstationary label field. The performance of proposed classification rule is validated by the values of local Bayes and empirical error rates realized by leave one out procedure. A simulation study for spatial covariance functions belonging to powered-exponential family and temporal covariance functions of AR(1) models is carried out. The influence of the values of spatial and temporal covariance parameters to error rates for several label field models are studied. The results showed that the proposed classification methodology can be applied successfully in practice with small error rates and can be a useful tool for discriminant analysis of spatio-temporal data.
, , Yonghong Wu, B. Wiwatanapataphee,
Nonlinear Analysis: Modelling and Control, Volume 26, pp 315-333; doi:10.15388/namc.2021.26.21202

Abstract:
In this paper, we study the solvability and asymptotic properties of a recently derived gyre model of nonlinear elliptic Schrödinger equation arising from the geophysical fluid flows. The existence theorems and the asymptotic properties for radial positive solutions are established due to space theory and analytical techniques, some special cases and specific examples are also given to describe the applicability of model in gyres of geophysical fluid flows.
Aili Zhang, Shuang Liu, Yang Yang
Nonlinear Analysis: Modelling and Control, Volume 26, pp 259-270; doi:10.15388/namc.2021.26.20948

Abstract:
This paper considers a by-claim risk model with constant interest rate in which the main claim and by-claim random vectors form a sequence of independent and identically distributed random pairs with each pair obeying some certain dependence or arbitrary dependence structure. Under the assumption of heavy-tailed claims, we derive some asymptotic formulas for ultimate ruin probability. Some simulation studies are also performed to check the accuracy of the obtained theoretical results via the crude Monte Carlo method.
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