Bifurcation of sign-changing solutions for one-dimensional \(p\)-Laplacian with a strong singular weight: \(p\)-superlinear at \(\infty \)
type: Item
instance of: scholarly article
title: Bifurcation of sign-changing solutions for one-dimensional \(p\)-Laplacian with a strong singular weight: \(p\)-superlinear at \(\infty \)
zbMATH Open document ID: 1232.34027
author: Juan-Miguel Gracia
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2011-10-17T00:00:00Z
review text: The authors investigate the one-dimensional \(p\)-Laplacian problem with a weight function \[ \varphi_p(u'(t))+\lambda h(t)f (u(t)) = 0 \text{ a.e. on }(0, 1),\;u(0) = u(1) = 0, \] where \(\varphi_p(s) = |s|^{p-2}s\), \(p>1\), \(\lambda\) is a nonnegative parameter, \(h\) is a nonnegative measurable function on \((0, 1)\), \(h\not\equiv 0\) on any open subinterval in \((0, 1)\) which may be singular at \(t = 0\) and/or \(t = 1\) and \(f\in C(\mathbb{R}, \mathbb{R})\). They obtain the existence, nonexistence, uniqueness and multiplicity of positive solutions as well as sign-changing solutions for the above problems.
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 5959647
zbMATH Keywords: \(p\)-Laplace equation
zbMATH Keywords: singular weight
zbMATH Keywords: Leray-Schauder degree
zbMATH Keywords: positive solutions
zbMATH Keywords: sign-changing solutions
reviewed by: Ruyun Ma
MaRDI profile type: Publication
full work available at URL: j.na.2011.03.058
OpenAlex ID: W4249896007
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DOI: 10.1016/J.NA.2011.03.058
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description: scientific article; zbMATH DE number 5959647