A.I. Santos

Higher order nonlinear two‐point boundary value problems with sign‐type Nagumo condition

In this paper we present existence and location results for two‐point boundary value problems for third and fourth order fully nonlinear differential equations.Nonlinearities are assumed to satisfy a sign‐type Nagumo condition which allows an asymmetric unbounded behavior. The arguments make use of lower and upper solutions method and degree theory.

Asymptotic Behaviour in a Certain Nonlinearly Perturbed Heat Equation: Non Periodic Perturbation Case

We consider a system described by the linear heat equation with adiabatic boundary conditions. We impose a nonlinear perturbation determined by a family of interval maps characterized by a certain set of parameters. The time instants of the perturbation are determined by an additional dynamical system, seen here as part of the external interacting system. We analyse the complex behaviour of the system, through the scope of symbolic dynamics, and the dependence of the behaviour on the time pattern of the perturbation, comparing it with previous results in the periodic case.