Existence of positive solutions to some nonlinear Neumann problems
type: Item
instance of: scholarly article
title: Existence of positive solutions to some nonlinear Neumann problems
zbMATH Open document ID: 0968.35049
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: The paper deals with nontrivial nonnegative solutions of the nonlinear Neumann problem \[ -\Delta u= b(x) u^{s-1}\quad\text{in }\Omega,\quad{\partial u\over\partial\nu}= a(x) u^{q-1}\quad\text{on }\partial\Omega. \] The solutions appear as critical points of the corresponding energy functional. A critical point is then obtained by using the first author's method [Sov. Math., Dokl. 20, 912-916 (1979; Zbl 0456.47053)] in the form \(u= r(v)v\), where \(v\) is a solution of a maximization problem with constraint and \(r(v)\) is a root of the associated bifurcation equation.
reviewed by: Radu Precup
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 1557547
zbMATH Keywords: critical points
zbMATH Keywords: maximization
zbMATH Keywords: bifurcation
author: S. I. Pokhozhaev
author: Alberto Tesei
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1557547