Exact number of positive solutions for a class of semipositone problems
type: Item
instance of: scholarly article
title: Exact number of positive solutions for a class of semipositone problems
zbMATH Open document ID: 1028.34027
DOI: 10.1016/S0022-247X(02)00539-5
author: Jiangang Cheng
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-27T00:00:00Z
review text: The author considers the nonlinear eigenvalue problem \[ y''(t)= \lambda(y^p(t)- y^q(t)),\quad 0< t< 1,\qquad y(-1)= y(1)= 0, \] where \(p> q> -1\), and \(\lambda> 0\) is a positive parameter. He gives a complete study to the exact number of positive solutions to the above problem. The proofs are based upon the time-maps estimate.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47J15
zbMATH DE Number: 1917767
zbMATH Keywords: boundary value problem
zbMATH Keywords: positive solution
zbMATH Keywords: existence
zbMATH Keywords: multiplicity
zbMATH Keywords: bifurcation
reviewed by: Ruyun Ma
MaRDI profile type: Publication
cites work: Evolution of positive solution curves in semipositone problems with concave nonlinearities
cites work: Asymptotic oscillations of continua of positive solutions of a semilinear Sturm-Liouville problem
cites work: Uniqueness of positive radial solutions for semilinear elliptic equations on annular domains
cites work: Exact number of solutions of a class of two-point boundary value problems involving concave and convex nonlinearities
cites work: A class of two-point boundary value problems
cites work: Exact multiplicity of positive solutions for a class of semilinear problem. II
cites work: An exact multiplicity theorem involving concave-convex nonlinearities and its application to stationary solutions of a singular diffusion problem
cites work: Uniqueness of positive radial solutions of the Dirichlet problems \(-\Delta u=u^ p\pm u^ q\) in an annulus
cites work: On the infinitely many positive solutions of a supercritical elliptic problem
full work available at URL: s0022-247x(02)00539-5
OpenAlex ID: W2046687838
description: scientific article; zbMATH DE number 1917767