Local existence of multiple positive solutions to a singular cantilever beam equation
type: Item
instance of: scholarly article
title: Local existence of multiple positive solutions to a singular cantilever beam equation
zbMATH Open document ID: 1191.34031
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-12-10T00:00:00Z
review text: The authors study existence and multiplicity of positive solutions to the fourth-order problem \[ u^{(4)}=q(t)f(t, u(t), u'(t)),\quad u(0)=u'(0)=u''(1)=u'''(1)=0, \] where \(q:(0,1)\rightarrow [0, \infty)\) is continuous with \(q(t)>0\) in \((0,1)\), \(f\) is allowed to be singular at \(t=0,~t=1\), ~\(u=0,~ v=0\). The main tool is the Guo-Krasnoselskii fixed point theorem in cones.
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5644912
zbMATH Keywords: existence
zbMATH Keywords: positive solutions
zbMATH Keywords: fourth-order problem
zbMATH Keywords: Guo-Krasnoselskii fixed point theorem
zbMATH Keywords: cones
author: Qingliu Yao
reviewed by: Ruyun Ma
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.07.043
OpenAlex ID: W2000209337
cites work: Q3732891
cites work: Existence and uniqueness theorems for fourth-order boundary value problems
cites work: Existence and uniqueness theorems for the bending of an elastic beam equation
cites work: Superlinear and sublinear focal boundary value problems
cites work: On two-point right focal eigenvalue problems
cites work: Right Focal Singular Boundary Value Problems
cites work: Singular \((p,n-p)\) focal and \((n,p)\) higher order boundary value problems
cites work: Twin solutions to singular boundary value problems
cites work: Multiplicity results for singular conjugate, focal, and \((N,P)\) problems
cites work: Multiple positive solutions for a semipositone fourth-order boundary value problem
cites work: Monotonically iterative method of nonlinear cantilever beam equations
cites work: Q3403793
cites work: Existence of positive solutions for non-positive higher-order BVPs
cites work: Existence of solutions to \((k,n-k-2)\) boundary value problems
cites work: Twin solutions to singular Dirichlet problems
cites work: Q4952887
cites work: Multiple solutions for a system of \((n_i p_i)\) boundary value problems
cites work: Multiple solutions and eigenvalues for third-order right focal boundary value problems
cites work: The existence and multiplicity of positive solutions for a third-order three-point boundary value problem.
cites work: Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem
cites work: Positive solutions for eigenvalue problems of fourth-order elastic beam equations.
cites work: Multiple positive solutions of conjugate boundary value problems with singularities.
cites work: Existence of \(n\) solutions and/or positive solutions to a semipositone elastic beam equation
cites work: Positive solutions of a singular nonlinear third order two-point boundary value problem
cites work: Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions
cites work: Positive solutions of a nonlinear elastic beam equation rigidly fastened on the left and simply supported on the right
cites work: Existence and multiplicity of positive solutions to a singular elastic beam equation rigidly fixed at both ends
cites work: Positive solutions of singular third-order three-point boundary value problems
cites work: Solvability of some fourth (and higher) order singular boundary value problems
cites work: Positive solutions of singular positone Dirichlet boundary value problems
cites work: Positive solutions to a class of singular sublinear two-point boundary value problems
cites work: A class of fourth order singular boundary value problems
DOI: 10.1016/J.JMAA.2009.07.043
Recommended article: Q4911289
Recommended article: Q3403793
Recommended article: Q5320561
Recommended article: Local existence and uniqueness of increasing positive solutions for non-singular and singular beam equation with a parameter
Recommended article: Existence and multiplicity of positive solutions to a singular elastic beam equation rigidly fixed at both ends
Recommended article: Q2951507
Recommended article: Q2994465
Recommended article: Existence and multiplicity of positive solutions for an elastic beam equation
Recommended article: Q4927604
Recommended article: Q3642363
description: scientific article; zbMATH DE number 5644912