This paper is concerned with the mixed H2/H∞ control problem for a class of stochastic time-varying systems with nonlinearities. The nonlinearities are described by statistical means and could cover several kinds of well-studied nonlinearities as special cases. The occurrence of the addressed nonlinearities is governed by two sequences of Bernoulli distributed white sequences with known probabi...

Thanks to a new upper bound, we study more precisely the nonlinearities of Maiorana-McFarland’s resilient functions. We characterize those functions with optimum nonlinearities and we give examples of functions with high nonlinearities. But these functions have a peculiarity which makes them potentially cryptographically weak. We study a natural super-class of Maiorana-McFarland’s class whose e...

in this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.

In this work, we study the weighted Kirchhoff problem \[ \begin{cases} g\big( \int_{B} (w(x) |\Delta u|^{2}) \, dx \big) [\Delta \Delta u)] = f(x,u) &\textrm{in $B$}, \\ u > 0 \frac{\partial u}{\partial n} &\textrm{on $\partial B$}, \end{cases} \] where $B$ is unit ball of $\mathbb{R}^{4}$, $w(x) \big( \log \frac{e}{|x|} \big)^{\beta}$, singular logarithm weight in Adam's embedding, $g$ a conti...

The objective of this work is to investigate a nonlocal problem involving singular and critical nonlinearities:\begin{equation*}\left\{\begin{array}{ll} ([u]_{s,p}^p)^{\sigma-1}(-\Delta)^s_p u = \frac{\lambda}{u^{\gamma}}+u^{ p_s^{*}-1 }\quad \text{in }\Omega,\\ u>0,\;\;\;\;\quad u=0,\;\;\;\;\quad }\mathbb{R}^{N}\setminus \Omega,\end{array} \right. \end{equation*} where $\Omega$ bounded domain ...

    M. and M.   Abstract: Existence and uniqueness of solution for singular 2-D systems depends on regularity condition. Simple regularity implies regularity and under this assumption, the generalized wave model (GWM) is introduced to cast singular 2-D system of equations as a family of non-singular 1-D models with variable structure.These index dependent models, along with a set of boundary co...

Biomechanical studies performed over the past thirty years have demonstrated that the simultaneous motion of human appendages exhibits significant coordination or “synergy” and that this dependence of the motion of seemingly independent body extremities is highly nonlinear. The present paper reports new experimental research conducted with a group of subjects for the case of coupled hand and fo...

The consensus tracking of singular multi-agent systems (MASs) with Lipschitz-type nonlinearities and exogenous disturbances is researched in this paper. Governed by a Markov chain, the network interaction randomly switches directed graph set, where spanning tree not contained each while exists union rooting at leader node. By utilizing collection in-neighbors’ information that involves communic...

We present a method to linearize, without approximation, specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the are expressed by scalar functions that defined quotient linear eigenvector. The exact linearization relies on an equivalent multiparameter problem (MEP) contains solutions NEPv. Due characterization MEPs in terms generalized this provides direct way co...

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...