We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical nonlinearity in general, possibly non-smooth, bounded domains.

This paper addresses the problem of controlling a certain class of continuous-time nonlinear systems subject to actuator saturations. The design of state feedback gains is done by considering a modelling of the nonlinear saturated system through deadzone nonlinearities satisfying a modified sector condition, which encompasses the classical sector-nonlinearity condition considered in previous wo...

We consider a class of two-dimensional integral equations with noncompact monotone Hammerstein operators and concave nonlinearity. prove constructive theorem on the existence uniqueness nontrivial nonnegative bounded solution study asymptotic behavior at infinity. Some examples kernels nonlinearity are given.

The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a compact global attractor for the solution semigroup of this equation is established. Moreover, the smoothness of the obtained attractor is also shown.

For a system A = (A1, . . . , An) of linear operators whose real linear combinations have spectra contained in a fixed sector in C and satisfy resolvent bounds there, functions f(A) of the system A of operators can be formed for monogenic functions f having decay at zero and infinity in a corresponding sector in R. In the case that the operators A1, . . . , An commute with each other and satisf...

An adaptive low-gain integral control framework is developed for tracking constant reference signals in a context of nite-dimensional, asymptotically stable, single-input, single-output linear systems subject to locally Lipschitz, monotone input and output nonlinearities of a general nature: the input nonlinearity is required to satisfy an asymptotic growth condition (of suucient generality to ...

On a bounded smooth domain Ω ⊂ R we study solutions of a semilinear elliptic equation with an exponential nonlinearity and a Hardy potential depending on the distance to ∂Ω. We derive global a priori bounds of the Keller–Osserman type. Using a Phragmen–Lindelöf alternative for generalized sub and super-harmonic functions we discuss existence, nonexistence and uniqueness of so-called large solut...

A new algorithm for nonparametric wavelet estimation of Hammerstein system nonlinearity is proposed. The algorithm works in the on-line regime (viz., past measurements are not available) and offers a convenient uniform routine for nonlinearity estimation at an arbitrary point and at any moment of the identification process. The pointwise convergence of the estimate to locally bounded nonlineari...

We investigate the existence of solutions of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition A2u + CAU = bu+ + f in 0, where R is a bounded open set in Rn with smooth boundary and the nonlinearity bu+ crosses eigenvalues of A2 + CA. We also investigate a relation between multiplicity of solutions and source terms of the equation with the nonlinearit...