Semilinear degenerate elliptic boundary value problems via critical point theory
type: Item
instance of: scholarly article
title: Semilinear degenerate elliptic boundary value problems via critical point theory
zbMATH Open document ID: 1271.35041
author: Kazuaki Taira
published in: Tsukuba Journal of Mathematics
publication date: 2013-02-21T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.tkbjm/1358777003
review text: In this paper the author studies a class of semilinear elliptic boundary value problems with degenerate boundary conditions which include as particular cases the Dirichlet and Robin problems. The author uses a variant of the Ljusternik-Schnirelman theory of critical points to prove results on the number of solutions to the problem under consideration. The results of this paper extend some earlier theorems due to Castro-Lazer to the degenerate case in the sense that the author also reduces an infinite dimensional problem to a finite dimensional one and then applies a finite dimensional critical point theory as in [\textit{A. Castro} and \textit{A. C. Lazer}, Ann. Mat. Pura Appl., IV. Ser. 120, 113--137 (1979; Zbl 0426.35038)]. Examples of nonlinear terms satisfying the assumptions are given in the text. All necessary background materials is also provided.
reviewed by: Marek Galewski
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 6137829
zbMATH Keywords: semilinear elliptic boundary value problem
zbMATH Keywords: degenerate boundary condition
zbMATH Keywords: multiple solution
zbMATH Keywords: critical point theory
zbMATH Keywords: Ljusternik-Schnirelman theory
MaRDI profile type: Publication
OpenAlex ID: W2240462752
DOI: 10.21099/TKBJM/1358777003
description: scientific article; zbMATH DE number 6137829