Multidimensional Dirichlet series in the problem of the asymptotics of spectral series of nonlinear elliptic operators
type: Item
instance of: scholarly article
title: Multidimensional Dirichlet series in the problem of the asymptotics of spectral series of nonlinear elliptic operators
zbMATH Open document ID: 0564.58035
DOI: 10.1007/BF02104897
author: V. P. Maslov
author: Sergei Yu. Dobrokhotov
published in: Journal of Soviet Mathematics
publication date: 1985-01-01T00:00:00Z
review text: This substantial paper is a contribution to the use of multidimensional Dirichlet series, and especially of the recent results of Leont'cev, to the construction and study of asymptotic solutions of boundary value problems for nonlinear elliptic equations. An important question is that of ''superposition'' of individual solutions, and the paper shows that, for broad classes of equations, these superposition laws can be expressed in terms of multidimensional Dirichlet series. The paper is divided in three main parts: (1) Dirichlet series in ordinary differential equations; (2) Asymptotic solutions of the generalized nonlinear Steklov problem for elliptic equations with variable coefficients, (3) Complex WKB method in boundary value problems of the type of the Steklov problem for nonlinear equations. Applications are given to equations of electroneutral semiconductors, sine-Gordon equations and Schrödinger equations.
reviewed by: Jean Mawhin
Mathematics Subject Classification ID: 58J32
zbMATH DE Number: 3899818
zbMATH Keywords: solitons
zbMATH Keywords: nonlinear elliptic equations
zbMATH Keywords: multidimensional Dirichlet series
zbMATH Keywords: Asymptotic solutions
zbMATH Keywords: generalized nonlinear Steklov problem
zbMATH Keywords: Complex WKB method
zbMATH Keywords: boundary value problems
zbMATH Keywords: electroneutral semiconductors
zbMATH Keywords: sine-Gordon equations
zbMATH Keywords: Schrödinger equations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3899818