We investigate the boundary growth of positive superharmonic functions u on a bounded domain Ω in R, n ≥ 3, satisfying the nonlinear elliptic inequality 0 ≤ −∆u ≤ cδΩ(x)u in Ω, where c > 0, α ≥ 0 and p > 0 are constants, and δΩ(x) is the distance from x to the boundary of Ω. The result is applied to show a Harnack inequality for such superharmonic functions. Also, we study the existence of posi...

This paper studies fuzzy filtering design for state estimation of nonlinear discrete-time systems with bounded but unknown disturbances. First, the Takagi and Sugeno fuzzy model is proposed to represent a nonlinear system. Next, using a linear matrix inequality (LMI) approach, the fuzzy filtering problems are characterized in terms of a linear matrix inequality problem (LMIP). The LMIP can be e...

This paper is concerned with the problem of robust static output feedback guaranteed cost control for a class of nonlinear discrete systems with mixed time-varying delays. The proposed controller uses the output measurement to robustly exponentially stabilize the closed-loop system and guarantee an adequate level of system performance. By constructing a set of improved Lyapunov-Krasovskii funct...

This paper considers local convergence of secant methods for a nonlinear system of equations. The well-known local convergence theory has been developed by Broyden, Dennis and Moré (1973). They used a norm inequality such that the difference between two vectors transformed by some matrix is bounded above by an order of one of the two. Instead, in the present paper, we use an inequality that bou...

A class of variational-hemivariational inequalities is studied in this paper. An inequality in the class involves two nonlinear operators and two nondifferentiable functionals, of which at least one is convex. An existence and uniqueness result is proved for a solution of the inequality. Continuous dependence of the solution on the data is shown. Convergence is established rigorously for finite...

I analyze the effect of inequality on economic growth in Latin America, where inequality is measured as the area of family farms as a percentage of the total area of agricultural holdings. Using data from 18 Latin American countries between 1960 and 2004, I find that inequality has a nonlinear effect on economic growth. Overall, for the countries included in this analysis, the share of family f...

We prove some concavity properties connected to nonlinear Bernoulli type free boundary problems. In particular, we prove a Brunn-Minkowski inequality and an Urysohn’s type inequality for the Bernoulli Constant and we study the behaviour of the free boundary with respect to the given boundary data. Moreover we prove a uniqueness result regarding the interior non-linear Bernoulli problem.

We prove a differential Harnack inequality for the Endangered Species Equation, which is a nonlinear parabolic equation. Our derivation relies on an idea related to the parabolic maximum principle. As an application of this inequality, we will show that positive solutions to this equation must blowup in finite time.