Nonlinear Analysis: Modelling and Control https://www.journals.vu.lt/nonlinear-analysis <p>Founded in 1997. Journal provides a multidisciplinary forum for scholars involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature.&nbsp;</p> Vilnius University Press en-US Nonlinear Analysis: Modelling and Control 1392-5113 <p>Please read the Copyright Notice in&nbsp;<a href="http://www.zurnalai.vu.lt/acta-paedagogica-vilnensia/journalpolicy">Journal Policy</a>.&nbsp;</p> Resilient H-infinity filtering for networked nonlinear Markovian jump systems with randomly occurring distributed delay and sensor saturation https://www.journals.vu.lt/nonlinear-analysis/article/view/22355 <p>The <em>H</em><sub>∞</sub> 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 <em>H</em><sub>∞</sub> 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.</p> Venkatesan Nithya Rathinasamy Sakthivel Yong Ren Copyright (c) 2021 Venkatesan Nithya | Rathinasamy Sakthivel | Yong Ren https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 187 206 10.15388/namc.2021.26.22355 Mittag–Leffler synchronization for impulsive fractional-order bidirectional associative memory neural networks via optimal linear feedback control https://www.journals.vu.lt/nonlinear-analysis/article/view/21203 <p>In this paper, we are concerned with the synchronization scheme for fractional-order bidirectional associative memory (BAM) neural networks, where both synaptic transmission delay and impulsive effect are considered. By constructing Lyapunov functional, sufficient conditions are established to ensure the Mittag–Leffler synchronization. Based on Pontryagin’s maximum principle with delay, time-dependent control gains are obtained, which minimize the accumulative errors within the limitation of actuator saturation during the Mittag–Leffler synchronization. Numerical simulations are carried out to illustrate the feasibility and effectiveness of theoretical results with the help of the modified predictor-corrector algorithm and the forward-backward sweep method.</p> Jiazhe Lin Rui Xu Liangchen Li Copyright (c) 2021 Jiazhe Lin | Rui Xu | Liangchen Li https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 207 226 10.15388/namc.2021.26.21203 Fourth-order elliptic problems with critical nonlinearities by a sublinear perturbation https://www.journals.vu.lt/nonlinear-analysis/article/view/20564 <p>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.</p> Lin Li Donal O’Regan Copyright (c) 2021 Lin Li | Donal O’Regan https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 227 240 10.15388/namc.2021.26.20564 Monotone iterative technique for time-space fractional diffusion equations involving delay https://www.journals.vu.lt/nonlinear-analysis/article/view/21656 <p>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.</p> Qiang Li Guotao Wang Mei Wei Copyright (c) 2021 Qiang Li | Guotao Wang | Mei Wei https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 241 258 10.15388/namc.2021.26.21656 Asymptotics for ultimate ruin probability in a by-claim risk model https://www.journals.vu.lt/nonlinear-analysis/article/view/20948 <p>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.</p> Aili Zhang Shuang Liu Yang Yang Copyright (c) 2021 Aili Zhang | Shuang Liu | Yang Yang https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 259 270 10.15388/namc.2021.26.20948 Tykhonov triples and convergence results for hemivariational inequalities https://www.journals.vu.lt/nonlinear-analysis/article/view/22429 <p>Consider an abstract Problem <em>P</em> in a metric space (<em>X</em>; <em>d</em>) assumed to have a unique solution <em>u</em>. The aim of this paper is to compare two convergence results <em>u'<sub>n</sub></em> → <em>u</em> and <em>u''<sub>n</sub></em> → <em>u</em>, both in <em>X</em>, and to construct a relevant example of convergence result <em>u<sub>n</sub></em> → <em>u</em> 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.</p> Rong Hu Mircea Sofonea Yi-Bin Xiao Copyright (c) 2021 Rong Hu | Mircea Sofonea | Yi-Bin Xiao https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 271 292 10.15388/namc.2021.26.22429 Analysis and simulation on dynamics of a partial differential system with nonlinear functional responses https://www.journals.vu.lt/nonlinear-analysis/article/view/22356 <p>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.</p> Yunfeng Jia Copyright (c) 2021 Yunfeng Jia https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 293 314 10.15388/namc.2021.26.22356 Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain https://www.journals.vu.lt/nonlinear-analysis/article/view/21202 <p>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.</p> Xinguang Zhang Lishan Liu Yonghong Wu B. Wiwatanapataphee Yujun Cui Copyright (c) 2021 Xinguang Zhang | Lishan Liu | Yonghong Wu | B. Wiwatanapataphee | Yujun Cui https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 315 333 10.15388/namc.2021.26.21202 Existence theorem for integral inclusions by a fixed point theorem for multivalued implicit-type contractive mappings https://www.journals.vu.lt/nonlinear-analysis/article/view/22357 <p>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.</p> Muhammad Usman Ali Ariana Pitea Copyright (c) 2021 Muhammad Usman Ali | Ariana Pitea https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 334 348 10.15388/namc.2021.26.22357 Radial symmetry for a generalized nonlinear fractional p-Laplacian problem https://www.journals.vu.lt/nonlinear-analysis/article/view/22358 <p>This paper first introduces a generalized fractional <em>p</em>-Laplacian operator (–Δ)<em><sup>s</sup></em><sub><em>F</em>;<em>p</em></sub>. 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 <em>p</em>-Laplacian, we study the monotonicity and radial symmetry of positive solutions of a&nbsp;generalized fractional <em>p</em>-Laplacian equation with negative power. In addition, a similar conclusion is also given for a&nbsp;generalized Hénon-type nonlinear fractional <em>p</em>-Laplacian equation.</p> Wenwen Hou Lihong Zhang Ravi P. Agarwal Guotao Wang Copyright (c) 2021 Wenwen Hou | Lihong Zhang | Ravi P. Agarwal | Guotao Wang https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 349 362 10.15388/namc.2021.26.22358 Classification of Gaussian spatio-temporal data with stationary separable covariances https://www.journals.vu.lt/nonlinear-analysis/article/view/22359 <p>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&nbsp; practice with small error rates and can be a useful tool for discriminant analysis of spatio-temporal data.</p> Marta Karaliutė Kęstutis Dučinskas Copyright (c) 2021 Marta Karaliutė | Kęstutis Dučinskas https://creativecommons.org/licenses/by/4.0 2021-03-01 2021-03-01 26 2 363 374 10.15388/namc.2021.26.22359