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**The Existence and Growth of Solutions for Several Systems of Complex Nonlinear Difference Equations**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (1)

This article is devoted to investigate some properties of solutions for several systems of complex differential-q-difference equations. Some results about the existence and the estimate for the growth of solutions for a series of systems of q-difference-differential equations are obtained. Moreover, it is a very satisfactory fact that some examples are given to illustrate the existence of solutions for such systems in each case of some results.

**Existence of Solutions to a Cahn-Hilliard Type Equation with a Logarithmic Nonlinear Term**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (1)

Our aim in this paper is to prove the existence of solutions to a Cahn-Hilliard type equation with a proliferation term and a logarithmic nonlinear term. Such an equation was proposed in view of biological applications. The main difficulty comes from the fact that we no longer have the conservation of the spatial average of the order parameter, contrary to the original Cahn-Hilliard equation. This makes the derivation of uniform (with respect to the regularization parameter) estimates on the solutions to approximated problems delicate, as blow up in finite time may occur.

**On Medium *-Clean Rings**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (1)

A *-ring R is called a medium *-clean ring if every element in R is the sum or difference of an element in its Jacobson radical and a projection that commute. We prove that a ring R is medium *-clean if and only if R is strongly *-clean and R/J(R) is a Boolean ring, Z3 or the product of such rings, if and only if R weakly J-*-clean and a2R is uniquely *-clean for all aR, if and only if every idempotent lifts modulo J(R), R is abelian and R/J(R) weakly *-Boolean. A subclass of medium *-clean rings with many nilpotents is thereby characterized.

**Convergence Properties of the Single-Step Preconditioned HSS Method for Non-Hermitian Positive Semidefinite Linear Systems**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (1)

For the nonsingular, non-Hermitian and positive semidefinite linear systems, we derive the convergence results of the single-step preconditioned HSS (SPHSS) method under suitable constraints. Additionally, we consider the acceleration of the SPHSS method by Krylov subspace methods and some spectral properties of the preconditioned matrix are established. Numerical experiments are presented to further examine the effectiveness of the proposed method either as a solver or a preconditioner.

**A Note on Sandwich Control Systems with Impulse Time Windows**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (2)

In this note, a sufficient condition for the stability of sandwich control systems with impulse time windows is derived. The proposed result is simpler than ones shown by Feng et al. (Int J Mach Learn Cybern 8:2009-2015, 2017). An example based on Chua's circuit is provided to confirm the effectiveness of the theoretical result.

**The Nonlinear Superposition Operators Between Zygmund-Type and Bloch-Type Spaces**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (2)

Let phi be a complex-valued function in the plane C. The superposition operator is defined by S phi(f)=phi degrees f. In this paper, we characterize the nonlinear superposition operators S phi acting between the Zygmund-type and Bloch-type spaces in terms of the order and type or the degree of phi.

**Existence and Multiplicity of Solutions for p(x)-Curl Systems Without the Ambrosetti-Rabinowitz Condition**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (2)

In this paper, we study the p(x)-curl systems: {... x |. x u| p(x)-2. xu + a(x)| u| p(x)-2 u = f (x, u), in O,. center dot u = 0, in O, |. x u| p(x)-2. xu x n = 0, u center dot n = 0, on. Omega, where O. R3 is a bounded simply connected domain with a C 1,1 boundary denoted by. O, p : O. (1,+8) is a continuous function, a. L 8 (O), and f : O x R3. R3 is a Carath ' eodory function. We use mountain pass theorem and symmetric mountain pass theorem to obtain the existence and multiplicity of solutions for a class of p(x)-curl systems in the absence of Ambrosetti-Rabinowitz condition.

**Coupled Coincidence Point and Fixed Point Results for Mixed Monotone Mappings and an Application to Integro-differential Equations**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (2)

In this paper, we propose some new coupled coincidence point and fixed point theorems for the mappings F and g. Our results are obtained by exploring the corresponding initial value problems for the mapping F and weakening the involved contractive conditions. As an application, we study the existence and uniqueness of solution to integro-differential equations.

**Discrete Nonselfadjoint Second-Order Two-Point Problems at Resonance**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (2)

Let T>2 be an integer, T={1,2,...,T}. We are considered with the discrete nonlinear two-point boundary value problem at resonanceis an eigenfunction of L corresponding to the principle eigenvalue nu(1).

**Indices of Maximal Invariant Subgroups and Solvability of Finite Groups**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (3)

Let A and G be finite groups and suppose that A acts coprimely on G via automorphisms. We study the solvability and supersolvability of G when certain proper maximal A-invariant subgroups of G have prime index or when they have certain prime power indices in G.

**Evolutionary Derivation of Sixth-Order P-stable SDIRKN Methods for the Solution of PDEs with the Method of Lines**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (3)

Evolutionary techniques are used for the derivation of a six-stage sixth-order singly diagonally implicit Runge-Kutta-Nystrom (SDIRKN) method for the integration of second-order initial value problems (IVPs). This method is P-stable and is recommended for stiff and mildly stiff problems possessing an oscillatory solution. It also attains an order which is one higher than existing methods of this type. Thus, it outperforms the other existing methods of this type when applied to relevant systems of IVPs arising from the semi-disrcetization of partial differential equations (PDEs) with the method of lines (MoL).

**Infinitely Many Solutions for p(x)-Laplacian-Like Neumann Problems with Indefinite Weight**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (3)

In the present paper, in view of the variational approach, we discuss the Neumann problems with indefinite weight and p(x)-Laplacian-like operators, originated from a capillary phenomena. Under certain assumptions, we prove the existence of infinitely many nontrival solutions of the problem.

**Some Results for a Class of Kirchhoff-Type Problems with Hardy-Sobolev Critical Exponent**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (3)

We study a class of Kirchhoff equations {-(a + b integral(Omega)vertical bar del u vertical bar(2) dx) Delta u = u(3)/vertical bar x vertical bar + lambda u(q), in Omega, u = 0, on partial derivative Omega, where Omega subset of R-3 is a bounded domain with smooth boundary and 0 is an element of Omega, a, b, lambda > 0, 0 < q < 1. By the variational method, two positive solutions are obtained. Moreover, when b > 1/A(1)(2) (A(1) > 0 is the best Sobolev-Hardy constant), using the critical point theorem, infinitely many pairs of distinct solutions are obtained for any lambda > 0.

**Almost Contact Metric Manifolds with Local Riemannian and Ricci Symmetries**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (4)

In this paper, we show that the Reeb sectional curvature of a locally symmetric almost coKahler manifold M2n+1 is a constant if and only if M2n+1 is locally isometric to the product of R and a locally symmetric almost Kahler manifold. Similar result in the framework of almost Kenmotsu manifolds is established. We give a characterization for a Ricci symmetric almost Kenmotsu manifold to be Einstein.

**Singularities of Dual Hypersurfaces and Hyperbolic Focal Surfaces Along Spacelike Curves in Light Cone in Minkowski 5-Space**

期刊： MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019; 16 (4)

In this paper, we consider spacelike curves in the light-cone 3-space that is canonically embedded in the light-cone 4-space and the de Sitter 4-space in Minkowski 5-space. To study the differential geometry of spacelike curves in the light cone, we propose a new type of frame, called the light-cone frame, moving along a spacelike curve. Concerning the framework of the theory of the Legendrian dualities between pseudo-spheres, the dual relationships between these spacelike curves and the light-cone dual hypersurface and the sphere-cone dual hypersurface are revealed. We respectively define the light-cone focal surface and the sphere-cone focal surface as the critical value sets of both the light-cone dual hypersurface and the sphere-cone dual hypersurface. It is also revealed that the projections of the critical value sets of both the light-cone focal surface and the sphere-cone focal surface along a spacelike curve are the hyperbolic evolute of the spacelike curve in the light cone. Using the classical unfolding theory, the singularities of these two hypersurfaces, the singularities of the hyperbolic evolute of the original curve, and the singularities of these two focal surfaces are differentiated using several equivalent conditions.