The existence and multiplicity of solutions for second-order impulsive differential equations on the half-line
type: Item
instance of: scholarly article
title: The existence and multiplicity of solutions for second-order impulsive differential equations on the half-line
zbMATH Open document ID: 1264.34051
author: Binxiang Dai
author: Dan Zhang
published in: Results in Mathematics
publication date: 2013-02-08T00:00:00Z
review text: The authors consider a boundary value problem for impulsive differential equations on the half-line \[ \begin{aligned} -\!u''(t) + u(t) &= \lambda f(t,u(t)) \quad \text{for a.e. } t \in [0,\infty),\\ \triangle u'(t_j) &= I_j(u(t_j)), \quad j = 1,\dotsc,p, \\ u^\prime(0+) &= g(u(0)), \quad u'(\infty) = 0, \end{aligned} \] where \(\lambda > 0\), \(f \in C([0,\infty)\times {\mathbb R};{\mathbb R})\), \(g\), \(I_j \in C({\mathbb R};{\mathbb R})\), \(0 < t_1 < \dotsb < t_p < \infty\). The authors obtain sufficient conditions for the existence of at least one and infinitely many solutions. Variational methods (especially the variant fountain theorem) are used.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 34B40
zbMATH DE Number: 6135238
zbMATH Keywords: impulsive differential equation
zbMATH Keywords: critical point theory
zbMATH Keywords: half-line
zbMATH Keywords: variant fountain theorem
MaRDI profile type: Publication
full work available at URL: s00025-011-0178-x
OpenAlex ID: W1964178637
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DOI: 10.1007/S00025-011-0178-X
description: scientific article; zbMATH DE number 6135238