We show optimal existence, nonexistence and regularity results for nonnegative solutions to Dirichlet problems as $$ \begin{cases} \displaystyle -\Delta_1 u = g(u)|D u|+h(u)f & \text{in}\;\Omega,\\ u=0 \text{on}\;\partial\Omega, \end{cases} where $\Omega$ is an open bounded subset of $\mathbb{R}^N$, $f\geq 0$ belongs $L^N(\Omega)$, $g$ $h$ are continuous functions that may blow up at zero. As a...

‎In this paper‎, ‎we study a class of boundary value problem‎ ‎involving the p-Laplacian oprator and singular nonlinearities‎. ‎We‎ ‎analyze the existence a critical parameter $lambda^{ast}$ such‎ ‎that the problem has least one solution for‎ ‎$lambdain(0,lambda^{ast})$ and no solution for‎ ‎$lambda>lambda^{ast}.$ We find lower bounds of critical‎ ‎parameter $lambda^{ast}$‎. ‎We use the method ...

The paper presents a procedure for identification continuous-time Hammerstein systems. To improve the representation of the nonlinear functions, the set of basis functions is iteratively refined. It is possible to identify the dominant nonlinearities, applying a singular value decomposition to the input matrix. In our approach, the linear dynamic subsystem is described by a transfer function of...

In this paper we show that a radially symmetric superlinear Dirichlet problem in a ball has infinitely many solutions. This result is obtained even in cases of rapidly growing nonlinearities, that is, when the growth of the nonlinearity surpasses the critical exponent of the Sobolev embedding theorem. Our methods rely on the energy analysis and the phase-plane angle analysis of the solutions fo...