Massimiliano Ferrara

Mathematical Programming with (Φ, ρ)-invexity

We introduce new invexity-type properties for differentiable functions, generalizing (F, ρ)-convexity. Optimality conditions for nonlinear programming problems are established under such assumptions, extending previously known results. Wolfe and Mond-Weir duals are also considered, and we obtain direct and converse duality theorems.

High-order moments conservation in thermostatted kinetic models

Recently the thermostatted kinetic framework has been proposed as mathematical model for studying nonequilibrium complex systems constrained to keep constant the total energy. The time evolution of the distribution function of the system is described by a nonlinear partial integro-differential equation with quadratic type nonlinearity coupled with the Gaussian isokinetic thermostat. This paper is concerned with further developments of this thermostatted framework. Specifically the term related to the Gaussian thermostat is adjusted in order to ensure the conservation of even high-order moments of the distribution function. The derived framework that constitutes a new paradigm for the derivation of specific models in the applied sciences, is analytically investigated. The global in time existence and uniqueness of the solution to the relative Cauchy problem is proved. Existence and moments conservation of stationary solutions are also performed. Suitable applications and research perspectives are outlined in the last section of the paper.

Controllability of a Nonholonomic Macroeconomic System

This paper studies optimal control problems and sub-Riemannian geometry on a nonholonomic macroeconomic system. The main results show that a nonholonomic macroeconomic system is controllable either by trajectories of a single-time driftless control system (single-time bang–bang controls), or by nonholonomic geodesics or by sheets of a two-time driftless control system (two-time bang–bang controls). They are strongly connected to the possibility of describing a nonholonomic macroeconomic system via a Gibbs–Pfaff equation or by four associated vector fields, based on a contact structure of the state space and our isomorphism between thermodynamics and macroeconomics that praises three laws of a nonholonomic macroeconomic system.

Multiplicity results for perturbed fourth-order Kirchhoff type elliptic problems

Using variational methods and critical point theory, we establish multiplicity results of nontrivial and nonnegative solutions for a perturbed fourth-order Kirchhoff type elliptic problem.

The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model

A further generalization of an economic growth model is the main topic of this paper. The paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when two time delays are inserted: the time employed in order that the capital is used for production and the necessary time so that the capital is depreciated. The existence of a unique nontrivial positive steady state of the generalized model is proved and sufficient conditions for the asymptotic stability are established. Moreover, the existence of a Hopf bifurcation is proved and, by using the normal form theory and center manifold argument, the explicit formulas which determine the stability, direction, and period of bifurcating periodic solutions are obtained. Finally, numerical simulations are performed for supporting the analytical results.

Multiplicity of solutions for a class of superlinear non-local fractional equations

In this paper, we are concerned with the problem driven by a non-local integro-differential operator with homogeneous Dirichlet boundary conditions. As a particular case, we study multiple solutions for the following non-local fractional Laplace equations:where is fixed parameter, is an open bounded subset of with smooth boundary () and is the fractional Laplace operator. By a variant version of the Mountain Pass Theorem, a multiplicity result is obtained for the above-mentioned superlinear problem without Ambrosetti–Rabinowitz condition. Consequently, the result may be looked as a complete extension of the previous work of Wang and Tang to the non-local fractional setting.

Qualitative Analysis of a Retarded Mathematical Framework with Applications to Living Systems

This paper deals with the derivation and the mathematical analysis of an autonomous and nonlinear ordinary differential-based framework. Specifically, the mathematical framework consists of a system of two ordinary differential equations: a logistic equation with a time lag and an equation for the carrying capacity that is assumed here to be time dependent. The qualitative analysis refers to the stability analysis of the coexistence equilibrium and to the derivation of sufficient conditions for the existence of Hopf bifurcations. The results are of great interest in living systems, including biological and economic systems.

New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations

Abstract In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to 814≈1.682

Variational approaches to impulsive elastic beam equations of Kirchhoff type

{8^{{\textstyle{1 \over 4}}}} \approx 1.682

Center Manifold Reduction and Perturbation Method in a Delayed Model with a Mound-Shaped Cobb-Douglas Production Function

. We describe the analysis of the proposed methods along with numerical experiments including comparison with the existing methods. Moreover, the attraction basins of the proposed methods are shown with some comparisons to the other existing methods.