Multiple unbounded solutions of boundary value problems for second-order differential equations on the half-line
type: Item
instance of: scholarly article
title: Multiple unbounded solutions of boundary value problems for second-order differential equations on the half-line
zbMATH Open document ID: 1021.34021
DOI: 10.1016/S0362-546X(01)00877-X
author: Baoqiang Yan
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-11-28T00:00:00Z
review text: The objective of the paper is to prove the existence of unbounded solutions to the following boundary value problem \((1/p(t))(p(t)x'(t))'+f(t,x(t))=0,\) \(t>0.\) Sufficient conditions are stated. The author considers a special Banach space \(C_\infty.\) To prove the results, the author relies on the nonlinear alternative and a theorem of Corduneanu. The existence of multiple unbounded solutions is also discussed using fixed-point index theory. Two examples are given to illustrate the results.
reviewed by: Abdelkader Boucherif
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 1836628
zbMATH Keywords: boundary value problems on the half-line
zbMATH Keywords: unbounded solutions
zbMATH Keywords: nonlinear alternative
zbMATH Keywords: Corduneanu theorem
zbMATH Keywords: fixed-point index
MaRDI profile type: Publication
cites work: Some new existence results for differential and integral equations
cites work: A fixed-point approach for nonlinear discrete boundary value problems
cites work: Existence and uniqueness for nonlinear boundary value problems on infinite intervals
cites work: Q3213489
cites work: Multiple positive solutions of impulsive nonlinear Fredholm integral equations and applications
cites work: Boundary value problems for impulsive integro-differential equations on unbounded domains in a Banach space
cites work: A Multiplicity Result for Periodic Solutions of Forced Nonlinear Second order Ordinary Differential Equations
cites work: Multiple periodic solutions for lagrangian systems in Tn
cites work: Q4886470
cites work: Q3994493
cites work: Q4286822
cites work: Existence theory for nonlinear Fredholm and Volterra integral equations on half-open intervals
cites work: Positive solutions to certain classes of singular nonlinear second order boundary value problems
cites work: Singular boundary value problems on a half-line
cites work: Q4897165
cites work: Solutions of impulsive boundary value problems on the half-line
Recommended article: Unbounded solutions of second-order multipoint boundary value problem on the half-line
Recommended article: Q4603361
Recommended article: Unbounded solutions of the singular boundary value problems for second order differential equations on the half-line
Recommended article: Multiple positive solutions for boundary value problems of second-order differential equations system on the half-line
Recommended article: Q5490870
Recommended article: Multiple positive solutions of the singular boundary value problems for second-order differential equations on the half-line
Recommended article: Q3585531
Recommended article: Q5385069
Recommended article: Unbounded solutions of BVP for second order ODE with \(p\)-Laplacian on the half line.
Recommended article: Q3431156
description: scientific article; zbMATH DE number 1836628