In this paper we study the powers under umbral composition and degeneration for Sheffer sequences, where we presented several applications related to Bernoulli polynomials, Frobenius-Euler polynomials, falling factorial polynomials and Bell polynomials and their degeneration cases. [ABSTRACT FROM AUTHOR]
MULTIPLICITY (Mathematics), BOUNDARY value problems, NONLINEAR theories, SYSTEMS theory, MATHEMATICAL analysis, MATHEMATICS
Abstract
Multiplicity results are obtained for systems of first order dynamic inclusions on time scales with the periodic boundary condition. To this aim, we introduce the notion of a strict solution-tube. We consider the case where the nonlinearity satisfies an upper semi-continuity condition. Our results are new even in the particular cases where the nonlinearity is single-valued or it has real values. [ABSTRACT FROM AUTHOR]