Nonlinear perturbations of linear elliptic systems at resonance

Passivity-Based Stability Analysis and Robust Practical Stabilization of Nonlinear Affine Systems with Non-vanishing Perturbations

This paper presents some analyses about the robust practical stability of a class of nonlinear affine systems in the presence of non-vanishing perturbations based on the passivity concept. The given analyses confirm the robust passivity property of the perturbed nonlinear systems in a certain region. Moreover, robust control laws are designed to guarantee the practical stability of the perturbe...

Elliptic Perturbations for Hammerstein Equations with Singular Nonlinear Term

We consider a singular elliptic perturbation of a Hammerstein integral equation with singular nonlinear term at the origin. The compactness of the solutions to the perturbed problem and, hence, the existence of a positive solution for the integral equation are proved. Moreover, these results are applied to nonlinear singular homogeneous Dirichlet problems.

On some nonlinear elliptic systems with coercive perturbations in R N

A nonlinear elliptic system involving the p-Laplacian is considered in the whole R N . Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established. 2000 Mathematics Subject Classification: 35J70, 35B45, 35B65.

Research Article Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance

Nonlinear Stochastic Perturbations of Dynamical Systems and Quasi-linear Parabolic PDE’s with a Small Parameter

In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes. In particular, we discuss the exit problem and metastability for the processes corresponding to quasi-linear initial-boundary value problems. 2000 Mathem...