Three positive solutions for delay differential equation BVPs with \(p\)-Laplacian on infinite interval
type: Item
instance of: scholarly article
title: Three positive solutions for delay differential equation BVPs with \(p\)-Laplacian on infinite interval
zbMATH Open document ID: 1205.34077
author: Yuming Wei
author: Weigao Ge
published in: Journal of Applied Mathematics and Computing
publication date: 2010-06-29T00:00:00Z
review text: The authors investigated the existence of three positive solutions for the boundary value problems of a delay differential equation with \(p\)-Laplacian on an infinite interval \[ (\phi_p(x'(t)))'+a(t)f(t, x, x', x_{t})=0, 0<t<\infty, \] \[ x_0=\xi, \alpha x(0)-\beta x'(0)=0, x'(\infty)=0, \] where \(\phi_p(s)=|s|^{p-2}s\), \(p>1\), \(\xi\in C([-r, 0]\), \({\mathbb R}^{+})\), both \(f: {\mathbb R}^{+}\times {\mathbb R}^{+}\times {\mathbb R}^{+}\times C([-r, 0], {\mathbb R}^{+})\to {\mathbb R}^{+}\) and \(a: {\mathbb R}^{+}\to {\mathbb R}^{+}\) are continuous, with \({\mathbb R}^{+}=[0, \infty)\), \(\alpha>0\), \(\beta\geq 0\), \(x'(\infty)=\lim_{t\to +\infty}x'(t)\). By using a fixed point point theorem in a cone introduced by Avery and Peterson, the existence of at least three positive solutions is obtained under suitable growth conditions imposed on the nonlinear term. An example is given to illustrate the feasibility of the main result.
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5728286
zbMATH Keywords: delay differential equations
zbMATH Keywords: boundary value problems
zbMATH Keywords: positive solutions
zbMATH Keywords: infinite interval
zbMATH Keywords: fixed point theorem
Wikidata QID: Q115377238
MaRDI profile type: Publication
full work available at URL: s12190-009-0273-2
OpenAlex ID: W2075564177
cites work: An infinite interval problem arising in circularly symmetric deformations of shallow membrane caps
cites work: Global solutions of a singular initial value problem to second order nonlinear delay differential equations
cites work: The monotone iterative technique for three-point second-order integrodifferential boundary value problems with \(p\)-Laplacian
cites work: Three positive fixed points of nonlinear operators on ordered Banach spaces
cites work: Q4335891
cites work: Q4332950
cites work: On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals.
cites work: Q5185568
cites work: Delay equations. Functional-, complex-, and nonlinear analysis
cites work: Boundary value problems for singular second-order functional differential equations
cites work: Existence of three positive solutions for \(m\)-point boundary-value problems with one-dimensional \(p\)-Laplacian
cites work: Q3994493
cites work: Introduction to functional differential equations
cites work: Multiple positive solutions to boundary value problems for second-order delay differential equations
cites work: Q4952140
cites work: Q4827143
cites work: Singular positone and semipositone boundary value problems of second order delay differential equations
cites work: Q5569338
cites work: Existence results for differential delay equations—II
cites work: Existence results for differential delay equations. I
cites work: Q5489947
cites work: Stabilization of vibrating beam with a tip mass controlled by combined feedback forces
cites work: Q4415626
cites work: Existence of solutions of a boundary value problem on the half-line to second order nonlinear delay differential equations
cites work: Q5430249
cites work: Q3591172
cites work: The expansion of a semigroup and a Riesz basis criterion
cites work: Triple positive solution to the one-dimensional \(p\)-Laplacian equation
DOI: 10.1007/S12190-009-0273-2
description: scientific article; zbMATH DE number 5728286