this paper is concerned with the study of the existence of positive solutions for a navier boundaryvalue problem involving the p-biharmonic operator; the right hand side of problem is a nonsmoothfunctional with variable parameters. the existence of at least three positive solutions is establishedby using nonsmooth version of a three critical points theorem for discontinuous functions. our resul...

We examine a nonlinear strongly resonant elliptic problem driven by the p-Laplacian and with a discontinuous nonlinearity. We assume that the discontinuity points are countable and at them the nonlinearity has an upward jump discontinuity. We show that the problem has at least two nontrivial solutions without using a multivalued interpretation of the problem as it is often the case in the liter...

A new approach to the cryptanalysis of symmetric algorithms based on nonsmooth optimisation is presented. We develop this technique as a novel way of dealing with nonlinearity over F2 by modeling the equations corresponding to the algorithm as a continuous optimisation problem that avoids terms of higher degree. The resulting problems are not continuously differentiable, but can be approached w...

Dither signals provide an effective way to compensate for nonlinearities in control systems. The seminal works by Zames and Shneydor, and more recently, by Mossaheb, present rigorous tools for systematic design of dithered systems. Their results rely, however, on a Lipschitz assumption relating to nonlinearity, and thus, do not cover important applications with discontinuities. This paper prese...

The existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via suband supersolution methods as well as variational techniques for nonsmooth functions. 2000 Mathematics subject classification: 35J20, 35J85, 49J40.

This paper is concerned with the study of the existence of positive solutions for a Navier boundaryvalue problem involving the p-biharmonic operator; the right hand side of problem is a nonsmoothfunctional with variable parameters. The existence of at least three positive solutions is establishedby using nonsmooth version of a three critical points theorem for discontinuous functions. Our resul...

In this paper, we present a new scheme to design adaptive controllers for uncertain systems containing nonsmooth nonlinearities in the actuator device. The control design is achieved by introducing certain well defined sign functions and Neural Networks approximations and by using the backstepping technique. For the design and implementation of the controller, no knowledge is assumed on the unk...

This paper is concerned with an optimal control problem governed by a semilinear, nonsmooth operator differential equation. The nonlinearity is locally Lipschitz-continuous and directionally differentiable, but not Gâteaux-differentiable. Two types of necessary optimality conditions are derived, the first one by means of regularization, the second one by using the directional differentiability ...