Sturm type problems for singular \(p\)-Laplacian boundary value problems.
type: Item
instance of: scholarly article
title: Sturm type problems for singular \(p\)-Laplacian boundary value problems.
zbMATH Open document ID: 1035.34013
DOI: 10.1016/S0096-3003(02)00031-0
author: Xiaojing Yang
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The author considers the following singular boundary value problem for the \(p\)-Laplacian operator: \(L_{p}u+\lambda c(t)u^{ (p-1)}=0\), \(0<t<1\), \(u(0)=u(1)=0\). Here, \(L_{p}u(t)=(a(t)u^{(p-1)})'\). The functions \(a^{-1}\) and \(c\) may be singular at t=0 and/or t=1. It is shown that there exists an increasing sequence of eigenvalues with a description of the corresponding eigenfunctions. As an application the author proves the existence of at least one solution for the nonresonance problem: \(L_{p}u(t)+f(t,u)=0\), \(u(0)=u(1)=0\).
reviewed by: Abdelkader Boucherif
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34B16
zbMATH DE Number: 1861380
zbMATH Keywords: Sturm theorem
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: singular boundary value problems
MaRDI profile type: Publication
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full work available at URL: s0096-3003(02)00031-0
OpenAlex ID: W1971251484
description: scientific article; zbMATH DE number 1861380