Publicación: (OMEGA,C)-ASYMPTOTICALLY PERIODIC FUNCTIONS, FIRST-ORDER CAUCHY PROBLEM, AND LASOTA-WAZEWSKA MODEL WITH UNBOUNDED OSCILLATING PRODUCTION OF RED CELLS
Fecha
2019
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MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Resumen
IN THIS PAPER, WE STUDY A NEW CLASS OF FUNCTIONS, WHICH WE CALL (OMEGA, C)-ASYMPTOTICALLY PERIODIC FUNCTIONS. THIS COLLECTION INCLUDES ASYMPTOTICALLY PERIODIC, ASYMPTOTICALLY ANTIPERIODIC, ASYMPTOTICALLY BLOCH-PERIODIC, AND UNBOUNDED FUNCTIONS. WE PROVE THAT THE SET CONFORMED BY THESE FUNCTIONS IS A BANACH SPACE WITH A SUITABLE NORM. FURTHERMORE, WE SHOW SEVERAL PROPERTIES OF THIS CLASS OF FUNCTIONS AS THE CONVOLUTION INVARIANCE. WE PRESENT SOME EXAMPLES AND A COMPOSITION RESULT. AS AN APPLICATION, WE PROVE THE EXISTENCE AND UNIQUENESS OF (OMEGA, C)-ASYMPTOTICALLY PERIODIC MILD SOLUTIONS TO THE FIRST-ORDER ABSTRACT CAUCHY PROBLEM ON THE REAL LINE. ALSO, WE ESTABLISH SOME SUFFICIENT CONDITIONS FOR THE EXISTENCE OF POSITIVE (OMEGA, C)-ASYMPTOTICALLY PERIODIC SOLUTIONS TO THE LASOTA-WAZEWSKA EQUATION WITH UNBOUNDED OSCILLATING PRODUCTION OF RED CELLS.
