The equation ut = ∆p(u 1/(p−1)) for p > 1 is a nonlinear generalization of the heat equation which is also homogeneous, of degree 1. For large time asymptotics, its links with the optimal Lp-Euclidean logarithmic Sobolev inequality have recently been investigated. Here we focuse on the existence and the uniqueness of the solutions to the Cauchy problem and on the regularization properties (hype...

Picone identity for a class of nonlinear differential equations is established and various qualitative results (such as Wirtinger-type inequality and the existence of zeros of first components of solutions) are obtained with the help of this new formula.

Trudinger and Moser, interested in certain nonlinear problems in differential geometry, showed that if |∇u|q is integrable on a bounded domain in R with q ≥ n ≥ 2, then u is exponentially integrable there. Symmetrization reduces the problem to a one-dimensional inequality, which Jodeit extended to q > 1. Carleson and Chang proved that this inequality has extremals when q ≥ 2 is an integer. Henc...

In this paper, the stability analysis and controller design for uncertain discretetime singularly perturbed system are investigated via a matrix inequality approach. In analysis, the stability condition under which the singularly perturbed system is quadratically stable for sufficiently small singular perturbation parameter is derived in the formulation of linear matrix inequality (LMI). In syn...

In this paper, we propose a concept of polynomiality for variational inequality problems and show how to find a near optimal solution of variational inequality problems in a polynomial number of iterations. To establish this result we build upon insights from several algorithms for linear and nonlinear programs (the ellipsoid algorithm, the method of centers of gravity, the method of inscribed ...

In this paper we study the optimal control of system driven by hemivariational inequality of second order. First, we establish the existence of solutions to hemivariational inequality which contains nonlinear pseudomonotone evolution operator. Introducing a control variable in the multivalued term of the generalized subdifferential, we prove the closedness (in suitable topologies) of the graph ...

This paper uses a cross-state panel for the United States over the 1976 to 2007 period to assess the relationship between income inequality and the inflation rate. Employing a semiparametric instrument variable (IV) estimator, we find that the relationship depends on the level of the inflation rate. A positive relationship occurs only if the states exceed a threshold level of inflation rate. Be...

This paper analyses the relationship between income inequality and growth in transition economies. The distinct and complex dynamics adherent to these economies lead to the proposition of new econometric models in the paper. However, empirical results do not support the proposed more flexible nonlinear functions. Further, the Kuznets hypothesis is clearly rejected by our data. On the contrary, ...

This paper investigates the problem of observer design for a class of nonlinear systems with timedelay and uncertain nonlinearity. Firstly, using the Mean-value Theorem and combining constructing the Lyapunov-Krasovskii functional, the convergence conditions of nonlinear observer for a class of nonlinear systems with time-varying delay and uncertain nonlinearity are established in terms of a li...