Multiplicity results for the 1-dimensional generalized \(p\)-Laplacian
type: Item
instance of: scholarly article
title: Multiplicity results for the 1-dimensional generalized \(p\)-Laplacian
zbMATH Open document ID: 0831.34032
author: Pedro Ubilla
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-06-19T00:00:00Z
review text: Of concern is the boundary value problem (P) \(- (a (|u' |^p) |u' |^{p - 2} u')' = f(u)\) in \(I = (0,1)\), \(u(0) = u(1) = 0\), where \(p > 1\), \(a \in C (\mathbb{R}^+)\), and \(f\) is a real continuous odd function. A weak solution to (P) is a function \(u \in W^{1, p}_0 (I)\) such that \(a(|u' |^p) |u' |^{p - 2} u' \in L^{p'} (I)\) \((p^{-1} + p'{}^{-1} = 1)\), and \(\int^1_0 [a (|u' |^p) |u' |^{p - 2} u' v' - f(u)v] = 0\), \(\forall v \in W^{1, p}_0 (I)\). The author discusses the existence and multiplicity of weak solutions of (P) by using an energy method.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 765145
zbMATH Keywords: boundary value problem
zbMATH Keywords: weak solution
zbMATH Keywords: existence
zbMATH Keywords: multiplicity
zbMATH Keywords: energy method
reviewed by: Sergiu Aizicovici
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1097
OpenAlex ID: W2085554323
DOI: 10.1006/JMAA.1995.1097
description: scientific article; zbMATH DE number 765145