Spectral asymptotics of nonlinear elliptic two-parameter problems
type: Item
instance of: scholarly article
title: Spectral asymptotics of nonlinear elliptic two-parameter problems
zbMATH Open document ID: 0974.35085
DOI: 10.1016/S0362-546X(99)00179-0
author: Tetsutaro Sihbata
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-12-18T00:00:00Z
review text: Spectral asymptotics is derived for a nonlinear two-parameter problem connected with the Laplace operator on three- and higher-dimensional domains, namely \(\Delta u+ \mu f(u)= \lambda g(u)\). The approach is different from that used by the author and by others for linear two-parameter problems. Under some specified assumptions on the nonlinear functions \(f\) and \(g\) the author first proves the existence of variational eigenvalues. Then the optimal estimates of \(\lambda(\mu)\) from above and below are derived. Finally, the author proves the fundamental theorem which gives the asymptotic formula showing the dependence of parameter \(\lambda\) on \(\mu\).
reviewed by: Pavel Burda
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35P30
zbMATH DE Number: 1539292
zbMATH Keywords: spectral asymptotics
zbMATH Keywords: two-parameter problem
zbMATH Keywords: nonlinear elliptic equation
zbMATH Keywords: estimation of eigenvalues
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1539292