Publicación: DICHOTOMY AND ALMOST AUTOMORPHIC SOLUTION OF DIFFERENCE SYSTEM
Fecha
2013
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Electronic Journal of Qualitative Theory of Differential Equations
Resumen
WE STUDY ALMOST AUTOMORPHIC SOLUTIONS OF RECURRENCE RELATIONS WITH VALUES IN A BANACH SPACE V FOR QUASILINEAR ALMOST AUTOMORPHIC DIFFERENCE SYSTEMS. ITS LINEAR PART IS A CONSTANT BOUNDED LINEAR OPERATOR ? DEFINED ON V SATISFYING AN EXPONENTIAL DICHOTOMY. WE STUDY THE EXISTENCE OF ALMOST AUTOMORPHIC SOLUTIONS OF THE NON-HOMOGENEOUS LINEAR DIFFERENCE EQUATION AND TO QUASILINEAR DIFFERENCE EQUATION. ASSUMING GLOBAL LIPSCHITZ TYPE CONDITIONS, WE OBTAIN MASSERA TYPE RESULTS FOR THESE ABSTRACT SYSTEMS. THE CASE WHERE THE EIGENVALUES ? VERIFY |?| = 1 IS ALSO TREATED. AN APPLICATION TO DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT IS GIVEN.
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MASSERA TYPE THEOREMS, BANACH SPACE, ALMOST AUTOMORPHIC SEQUENCES
