Discontinuous almost periodic type functions, almost automorphy of solutions of differential equations with discontinuous delay and applications

• Main Authors: Alan Chávez, Samuel Castillo, Manuel Pinto
• Format: Article
• Language: English
• Published: University of Szeged 2015-01-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: almost automorphic functions; difference equations; differential equation with piecewise constant argument; exponential dichotomy
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=3340
• ISSN: 1417-3875; 1417-3875

In this work, using discontinuous almost periodic type functions, exponential dichotomy and the notion of Bi-almost automorphicity we give sufficient conditions to obtain a unique almost automorphic solution of a quasilinear system of differential equations with piecewise constant arguments. Finally, an application to the Lasota–Wazewska model with piecewise constant delayed argument is given.