منابع مشابه
Functional Equations for Higher Logarithms
Following earlier work by Abel and others, Kummer gave functional equations for the polylogarithm function Lim(z) up to m = 5 in 1850, but no example for larger m was known until recently. We give the first genuine 2-variable functional equation for the 7–logarithm. We investigate and relate identities for the 3-logarithm given by Goncharov and Wojtkowiak and deduce a certain family of function...
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The (multivalued) higher logarithms are interpreted, by studying their monodromy, as giving well-defined maps from P¿ — (3 points} into certain complex nilmanifolds with C*-actions. The purpose of this note is to exhibit a family of unipotent representations of Z * Z arising naturally from the monodromy of the higher logarithms ln¿. (see [4]), and thereby interpret each ln¿. as yielding a well-...
متن کاملPOSITIVE PERIODIC SOLUTIONS FOR HIGHER-ORDER FUNCTIONAL q-DIFFERENCE EQUATIONS
In this paper, using the recently introduced concept of periodic functions in quantum calculus, we study the existence of positive periodic solutions of a certain higher-order functional q-difference equation. Just as for the well-known continuous and discrete versions, we use a fixed point theorem in a cone in order to establish the existence of a positive periodic solution. This paper is dedi...
متن کاملOscillation Theorems for Certain Higher Order Nonlinear Functional Differential Equations
Some new oscillation theorems for higher-order nonlinear functional differential equations of the form d n dt n a(t) d n x(t) dt n α + q(t)f x g(t) = 0, α > 0, are established.
متن کاملPositive periodic solutions for higher order functional difference equations
In this paper, we apply a fixed point theorem to obtain sufficient conditions for the existence of positive periodic solutions for two classes of higher-order functional difference equations. AMS subject classification: 39A10.
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2003
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-003-0312-z