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Details van artikel 179 van 269 gevonden artikelen
| Titel: |
On the convergence of power series those coefficients satisfy a poincare type linear and nonlinear difference equation |
| Auteur: |
Ifantis, Evangelos K. |
| Verschenen in: |
Complex variables and elliptic equations |
| Paginering: | Jaargang 9 (1987) nr. 1 pagina's 63-80 |
| Jaar: |
1987-10 |
| Inhoud: |
Nonlinear difference equations of the form [image omitted] [image omitted] are studied under suitable assumptions on the function G(w) and the roots of the polynomial [image omitted] . Equation (I) is reduced to an operator equation of the form [image omitted] where g1 is a fixed element in an abstract. Banach space H1 and depends on the initial conditions (f(i) = λii=1, 2….k of (I). The existence of a solution f of (II) in H1 means that there exists a solution f(n) of (I) such that the power series [image omitted] converges absolutely for |z|≤.1. In the case of the linear homogeneous or inhomogeneous equation [image omitted] the nonlinear operator N1 in (II) is a constant mapping in H1 and (II) gives the abstract form f of the unique solution f(n). A theorem for the existence of solutions of (IV) in the Hilbert space l2 (1,∞) and the Banach space l1(1∞) follows immediately from this result. Two corollaries to this theorem predict the radius of convergence of the series (III) and a third corollary predicts the existence of “chaotic motion” in a class of nonhomogeneous linear difference equations. For the case, where the function G(w) is analytic, it is shown that the nonlinear operator, is a holomorphis map in an open sphere of H1. This proves the existence of solutions in l1(1, ∞) of the more general nonlinear equation [image omitted] under suitable assumptions on the sequences ck(n)k = 1,2,…. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 179 van 269 gevonden artikelen
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