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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/8899

Title: Nonlinear Equations with Infinitely many Derivatives
Authors: Gorka, P.
Prado, H.
Reyes, E.G.
Issue Date: 2011
Publisher: COMPLEX ANALYSIS AND OPERATOR THEORY Volume: 5 Issue: 1 Pages: 313-323 DOI: 10.1007/s11785-009-0043-z Published: MAR 2011
Abstract: We study the generalized bosonic string equation Delta e(-c) (Delta)phi = U(x, phi), c > 0 on Euclidean space R(n). First, we interpret the nonlocal operator Delta e(-c) (Delta) using entire vectors of Delta in L(2)(R(n)), and we show that if U(x, phi) = phi(x) + f (x), in which f is an element of L(2)(R(n)), then there exists a unique real-analytic solution to the Euclidean bosonic string in a Hilbert space H(c,) (infinity) (R(n)) we define precisely below. Second, we consider the case in which the potential U(x, phi) in the generalized bosonic string equation depends nonlinearly on phi, and we show that this equation admits real-analytic solutions in H(c,infinity)(R(n)) under some symmetry and growth assumptions on U. Finally, we show that the above given equation admits real-analytic solutions in H(c,infinity)(R(n)) if U(x, phi) is suitably near U(0)(x, phi) = phi, even if no symmetry assumptions are imposed.
Description: Gorka, P. Univ Talca, Inst Matemat & Fis, Talca, Chile
URI: http://dspace.utalca.cl/handle/1950/8899
ISSN: 1661-8254
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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