This paper investigates the solvability and dynamic properties of the following multidimensional close-to-cyclic system of nonlinear difference equations yn+1 (i) = aiyn (i+1) (y n−k (i+1)) pi+1 + b i (yn−k+1 (i)) pi ;n ∈ ℕ0, where yn (i+k) = yn (i),pi+k = pi,ai+k = ai,bi+k = bi;i = 1,k¯, the initial values y−k (i), y−k+1 (i), …,y0 (i) and ai and bi, i = 1,k¯, are positive real numbers and pi, i = 1,k¯, are real numbers. The system, characterized by intricate nonlinear interactions, is analyzed to derive explicit solutions and examine its asymptotic behavior. By leveraging a transformation approach, the multidimensional system is reduced to a simpler form, allowing for a comprehensive analysis of its solutions. The study demonstrates that under specific conditions, the system’s equilibrium points are globally attractive, ensuring stability. The theoretical findings are supported by numerical examples that highlight the behavior of solutions under various parameter configurations, illustrating the practical applicability of the results.

In this paper, we consider fractional Hardy-Hénon parabolic equations driven by fractional Brownian motion. The local existence and uniqueness of Lq mild solutions are proved.

With the purpose of applying the Łukasiewicz fuzzy set to sub-hoop in hoops, the concept of Łukasiewicz fuzzy sub-hoop is introduced, and its properties are investigated. The relationship between fuzzy sub-hoop and Łukasiewicz fuzzy sub-hoop are discussed. Conditions for Łukasiewicz fuzzy set to be a Łukasiewicz fuzzy sub-hoop are provided, and characterizations of Łukasiewicz fuzzy sub-hoop are displayed. Conditions under which ∈-set, q-set, and O-set can be sub-hoops are investigated.

In contrast to most other periodically forced chaotic systems with infinitely many isolated coexisting strange attractors, little seems to be known about the ones that possess conjoined Lorenz-like attractors with potential existence of infinitely many pairs of wings/scrolls. To achieve this target, this note proposes a new periodically forced extended Lorenz-like system, which generates infinitely many singularly degenerate heteroclinic cycles or heteroclinic orbits to any two equilibria of a family of non-hyperbolic lines, the collapses of which create not only the desirable conjoined Lorenz-like attractors, but also infinitely many isolated coexisting ones. What is more, the state variable x of that conjoined Lorenz-like attractor presents stochastic behaviors, confirming the links between long period and chaos. This also generalizes the classical concept of boundedness of chaos, i.e., the system orbits beginning from one sub-two-scroll of that conjoined Lorenz-like attractor might tend to the ones at infinity. Apart from those, the existence of an invariant surface and a family of infinitely many pairs of symmetrical heteroclinic orbits are proved by utilizing the Lyapunov function, the definitions of both α-limit set and ω-limit set.

In the present paper, we give the bounds for the second Hankel determinant of the logarithmic coefficients of a certain subclass of normalized univalent functions, which we have introduced here. Relevant connections of the results, which we have presented here, with those available in the existing literature are also described briefly.

In this work, the existence of a polynomial system of degree four with an invariant triangle containing at least four small-amplitude limit cycles is proved. This result improves the result obtained in [2].

This work is devoted to the study of multiplicity results of solutions for a class of nonlinear equations involving the square root of the Laplacian. Indeed, we will use variational methods for smooth functionals, defined on reflexive Banach spaces, in order to achieve the existence of at least three solutions for the equations. Moreover, assuming that the nonlinear terms are nonnegative, we will prove that the solutions are nonnegative. Finally, by presenting an example, we will ensure the applicability of our results.

In this paper, we study the character values of homogeneous monotonic P-polynomial table algebras with finite dimension d ≥ 5. To this end, we obtain a trigonometric polynomial to calculate the eigenvalues of the first intersection matrix of these table algebras using the z-transform. Finally by applying some methods for tridiagonal matrices, the character values of these table algebras are given in terms of Chebyshev polynomials.

In this paper, we are concerned with a logarithmic nonlinear viscoelastic m(x)-biharmonic equation. Firstly, we proved the local existence of solutions by using the Faedo-Galerkin method. Later, we proved the blow up of solutions by using the concavity method.

In this paper, we consider integral boundary value problems of nonlinear fractional differential equations. Existence results of positive solutions for the problem are obtained based on the Guo-Krasnoselskii theorem and the Five functional fixed point theorem. Simple examples follow the main results in successive sections.