Application of Morse theory for some damped Dirichlet nonlinear impulsive differential equations
type: Item
instance of: scholarly article
title: Application of Morse theory for some damped Dirichlet nonlinear impulsive differential equations
zbMATH Open document ID: 1497.34051
author: Junjun Zhou
author: Xiao Bie
author: Yangyang Wang
published in: Differential Equations and Dynamical Systems
publication date: 2022-03-16T00:00:00Z
review text: The authors consider Dirichlet problem for second order ODE with impulses at fixed times \[ -u''(t) + g(t)u'(t) + \lambda u(t) = f(t,u(t)) \text{ for a.e.}\ t \in [0,T], \] \[ \Delta u'(t_j) = I_j(u(t_j)), \quad j = 1,2,\ldots,p, \] \[ u(0) = u(T) = 0, \] with \(0 < t_1 < t_2 < \cdots < t_p < T\), continuous coefficient \(g\), right-hand side \(f\) and impulse functions \(I_j\). Sufficient conditions ensuring the existence of at least three nontrivial solutions are obtained using Morse theory. Illustrating examples are also given.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 58E50
zbMATH DE Number: 7491025
zbMATH Keywords: Dirichlet boundary value problem
zbMATH Keywords: impulsive effects
zbMATH Keywords: variational methods
zbMATH Keywords: nontrivial solutions
zbMATH Keywords: Morse theory
MaRDI profile type: Publication
full work available at URL: s12591-017-0400-8
OpenAlex ID: W2765485604
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DOI: 10.1007/S12591-017-0400-8
description: scientific article; zbMATH DE number 7491025