Desigualdades de Lyapunov para edos con diferentes condiciones de contorno

Abstract

The objective of this work is to study the definition and main properties of Lp Lyapunov constants, 1 ≤ p ≤ ∞, for scalar ordinary differential equations with different boundary conditions, although we deal with more details Neumann boundary conditions. We will focus on the study of the characterization of such constant as a minimum of some special minimization problem. It includes linear resonant problems, but at the end of this work, we use the linear results to study nonlinear resonant problems, specific with Neumann boundary conditions. To study all these problems, we have used differents techniques of Functional Analysis.