Publicación: DISCONTINUOUS ALMOST AUTOMORPHIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS
Fecha
2014
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Editor
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
Resumen
IN THIS ARTICLE WE INTRODUCE A CLASS OF DISCONTINUOUS ALMOST AUTOMORPHIC FUNCTIONS WHICH APPEARS NATURALLY IN THE STUDY OF ALMOST AUTOMORPHIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT. THEIR FUNDAMENTAL PROPERTIES ARE USED TO PROVE THE ALMOST AUTOMORPHICITY OF BOUNDED SOLUTIONS OF A SYSTEM OF DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT. DUE TO THE STRONG DISCRETE CHARACTER OF THESE EQUATIONS, THE EXISTENCE OF A UNIQUE DISCRETE ALMOST AUTOMORPHIC SOLUTION OF A NON-AUTONOMOUS ALMOST AUTOMORPHIC DIFFERENCE SYSTEM IS OBTAINED, FOR WHICH CONDITIONS OF EXPONENTIAL DICHOTOMY AND DISCRETE BI-ALMOST AUTOMORPHICITY ARE FUNDAMENTAL.
