Existence of a positive solution with concave and convex components for a system of boundary value problems

We prove the existence of at least one positive solution for a system of two nonlinear second-order differential equations with nonlocal boundary conditions. One component of the solution is a concave function, and the other one is a convex function. A recent hybrid Krasnosel’skiĭ–Schauder fixed point theorem is used to prove the existence of a positive solution. To illustrate the applicability of the obtained result, an example is considered

A new dynamic model for simultaneous saccharification and fermentation process of rice wine

In this paper, a new fractional model for the simultaneous saccharification and fermentation process of rice wine is proposed. To begin with, the existence and uniqueness of solution to the new model are proved by using some fixed point theorems. In addition, the stability at the equilibrium point and the Ulam–Hyers stability of the fractional simultaneous and saccharification fermentation model are analyzed. Then the approximate solutions of the fractional simultaneous saccharification and fermentation model are obtained by using the generalised Euler method. Finally, numerical simulations are given to verify the rationality of the fractional simultaneous saccharification and fermentation model. The new model proposed in this paper can more sensitively capture changes in the reaction

On stability and convergence of difference schemes for one class of parabolic equations with nonlocal condition

In this paper, we construct and analyze the finite-difference method for a two-dimensional nonlinear parabolic equation with nonlocal boundary condition. The main objective of this paper is to investigate the stability and convergence of the difference scheme in the maximum norm. We provide some approaches for estimating the error of the solution. In our approach, the assumption of the validity of the maximum principle is not required. The assumption is changed to a weaker one: the difference problem’s matrix is the M-matrix. We present numerical experiments to illustrate and supplement theoretical results

Soliton stability and topological invariants in a generalized nonlinear Klein–Gordon equation: Existence, dynamics, and conservation laws

This paper investigates the stability and dynamical behavior of soliton solutions in generalized nonlinear Klein–Gordon equations defined on higher-dimensional manifolds. We establish the existence of stable multisoliton configurations using variational methods and demonstrate their stability under small perturbations through energy estimates and topological considerations. Furthermore, we explore topological invariants (particularly, the topological charge) in preventing certain types of instabilities and ensuring the long-term persistence of solitons

Effect of gravity on the pattern formation in aqueous suspensions of luminous Escherichia coli

This paper presents a nonlinear two-dimensional-in-space mathematical model of self-organization of aqueous bacterial suspensions. The reaction–diffusion–chemotaxis model is coupled with the incompressible Navier–Stokes equations, which are subject to a gravitational force proportional to the relative bacteria density and include a cut-off mechanism. The bacterial pattern formation of luminous Escherichia coli is modelled near the inner lateral surface of a circular microcontainer, as detected by bioluminescence imaging. The simulated plume-like patterns are analysed to determine the values of the dimensionless model parameters, the Schmidt number, Rayleigh number and oxygen cut-off threshold, that closely match the patterns observed experimentally in a luminous E. coli colony. The numerical simulation at the transient conditions was carried out using the finite difference technique

Finite-time synchronization and quasi-synchronization of fractional-order fuzzy BAM neural networks with time delays

This paper concentrates on the finite-time synchronization (FTS) and the quasi-synchronization (QS) problems for a kind of fractional-order fuzzy BAM neural networks with time delays (FOFBAMNNs). In order to reach the goals of synchronization, two novel controllers are designed. Then, based on finite-time stability theorem, Lyapunov function theory, and several inequality techniques, through the application of two different designed controllers, several criteria for both FTS and QS are established. Moreover, more precise error level and settling times are given. The effectiveness of the derived criteria is ultimately validated through two simulations

A revisit to tail risk measures in the presence of bivariate regularly varying tailed insurance and financial risks

Consider a discrete-time insurance risk model in which the one-period insurance and financial risks are assumed to be independent and identically distributed random pairs, but a strong dependence structure is allowed to exist between each pair. Recently, Q. Tang and Y. Yang employed a framework of bivariate regular variation to model the heavy tails and the dependence of the insurance and financial risks, and they also established an asymptotic formula for the finite-time ruin probability [Interplay of insurance and financial risks in a stochastic environment, Scand. Actuar. J., 2019(5):432–451, 2019]. In this paper, by adopting a different approach, we study the asymptotic behavior of some tail risk measures for the aggregate discounted net loss, including the tail probability and the conditional loss-based tail expectation. We show both analytically and numerically how the heavy tailedness and the dependence of each pair of insurance and financial risks affect the tail risk measures

A class of nonlinear double-phase Dirichlet fractional differential equations

In this paper, we study the existence of positive solutions for a new class of double-phase Dirichlet fractional differential equations with singular and superlinear terms. By applying the Nehari manifold method we show that for all small values of the parameter τ > 0, the considered equation has at least two positive solutions

M-matrices and one-dimensional discrete Sturm–Liouville problems with nonlocal boundary conditions

This article is the second part of a survey dedicated to M-matrices and the application of the finite difference method to elliptic problems with nonlocal boundary conditions. Here, we examine cases in which the matrix of the resulting system of linear equations is an M-matrix. Here, we address the discrete Sturm–Liouville problem with nonlocal boundary conditions, describing its spectrum in one-dimensional case. This enables us to determine the values of the nonlocality parameters for which the finite difference scheme is represented by an M-matrix

On a novel type of generalized simulation functions with fixed point results for wide Ws-contractions

One of the most significant hypotheses in fixed point theory is the nonexpansivity condition of contractive mappings. This property is crucial as operators that do not satisfy this criterion may lack fixed points. In this paper, we propose a novel condition that, within the appropriate framework, can obviate the necessity of imposing the nonexpansivity requirement in the initial hypotheses. By employing this new condition, we illustrate how innovative results can be derived in this area. Finally, we examine the existence and uniqueness of a solution for an elastic beam equation with nonlinear boundary conditions grounded in the introduced fixed point results