Exact multiplicity results for a \(p\)-Laplacian problem with concave--convex--concave nonlinearities
type: Item
instance of: scholarly article
title: Exact multiplicity results for a \(p\)-Laplacian problem with concave--convex--concave nonlinearities
zbMATH Open document ID: 1026.34027
DOI: 10.1016/S0362-546X(02)00298-5
author: Idris Addou
author: Shin-Hwa Wang
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-04-28T00:00:00Z
review text: The authors study the exact number of positive solutions to the two-point Dirichlet boundary value problem \[ -\biggl(\varphi_p \bigl(u'(x) \bigr) \biggr)'= \lambda f\bigl(u (x)\bigr),\;-1<x<1, \quad u(-1)= u(1)=0, \] where \(p>1\), \(\varphi_p(y) =|y|^{p-2} y\), \(f\in C^2(0,\infty)\) satisfies \(f(0)=0\) and has at least two distinct simple positive zeros \(b<c\) and \(f''\) changes sign more than twice on \((0,\infty)\). The main tool they used is the time-map method.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1901883
zbMATH Keywords: exact multiplicity result
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: concave-convex-concave
zbMATH Keywords: nonlinearity
zbMATH Keywords: positive solution
zbMATH Keywords: dead-core solution
zbMATH Keywords: bifurcation
zbMATH Keywords: time-map
reviewed by: Ruyun Ma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1901883