Anderson L. A. de Araujo

A note on immersions of domains of fractional powers of certain sectorial operators in Sobolev spaces

Abstract In this note we give a proof of a result on immersions of domains of fractional powers of certain sectorial operators associated to strongly elliptic operators in Sobolev spaces; such immersions preserve information on fractional derivatives. We also briefly comment on the application of this result to a problem of optimal control of mosquito populations.

Some results on Riccati equations, Floquet theory and applications

In this paper, we present two new results to the classical Floquet theory, which provides the Floquet multipliers for two classes of the planar periodic system. One of these results provides the Floquet multipliers independently of the solution of system. To demonstrate the application of these analytical results, we consider a cholera epidemic model with phage dynamics and seasonality incorporated.

The Mean Curvature Equation with Oscillating Nonlinearity

Abstract We find a solution of the Dirichlet problem for the prescribed mean curvature equation in Ω with u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝN, N ≥ 1 and f : Ω × [0,∞) → ℝ is an unbounded continuous function with oscillatory behavior near the origin.