Almost periodicity in hereditary systems of second order

• Grant number: 09/01821-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2009
• End date: May 31, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Eduardo Alex Hernández Morales
• Grantee: Andréa Cristina Prokopczyk Arita
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The objective of this work is to study the existence of almost and asymptotically almost periodic solutions for a class of functional differential equations of second order described in the formd^{2}/dt^{2}(x(t)-g(t,x_{t},x'(t)))=Ax(t)+f(t,x_{t},x'(t)), t\in[0,a],x_{0}=\varphi\in B,x'(0)=\xi\in X,where A is a infinitesimal generator of a strongly continuous coseno function on a Banach space X, B is a phase space described axiomatically and f, g are appropriate functions.