Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying dif...

In this paper, we introduce an innovative and systematic technique to study delay differential equations via polynomials. First, we review an intrinsic relation between delay differential equations and polynomials. From this relation, we obtain long time behaviors of the solutions to delay differential equations via asymptotic analysis of the corresponding polynomials. Moreover, we derive asymp...

This paper studies the stability of large-scale impulsive delay differential systems and impulsive neutral systems. By developing some impulsive delay differential inequalities and a comparison principle, sufficient conditions are derived for the stability of both linear and nonlinear large-scale impulsive delay differential systems and impulsive neutral systems. Examples are given to illustrat...

Weboth propose and test an implicit strategy that is based on changing the search space from points to directions, which in combination with the Differential Evolution (DE) algorithm, is easily implemented for solving boundary optimization of a generic continuous function. In particular, we see that the DEmethod can be efficiently implemented to find solutions on the boundary of a convex and bo...

This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some ot...

OuIang inequalities and their generalizations have proved to be useful tools in oscillation theory, boundedness theory, stability theory, and other applications of differential and difference equations. A nice introduction to continuous and discrete OuIang inequalities can be found in 1, 2 , and studies in 3–5 give some of their generalizations to multiple integrals and higher-dimensional space...

In this paper, we obtain some new results about weakly singular integral inequalities. These inequalities are used to establish the global existence and uniqueness for fractional differential equations of Riemann–Liouville type. Some examples provided illustrate applicability our main results.

BACKGROUND Interventions to promote healthy eating make a potentially powerful contribution to the primary prevention of non communicable diseases. It is not known whether healthy eating interventions are equally effective among all sections of the population, nor whether they narrow or widen the health gap between rich and poor. We undertook a systematic review of interventions to promote heal...

In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...

We establish the local and global two-weight Poincaré inequalities for differential forms in Ls(μ)-averaging domains. c © 2007 Elsevier Ltd. All rights reserved.