An application of variational methods to Dirichlet boundary value problem with impulses
type: Item
instance of: scholarly article
title: An application of variational methods to Dirichlet boundary value problem with impulses
zbMATH Open document ID: 1191.34039
author: Ziheng Zhang
author: Rong Yuan
published in: Nonlinear Analysis. Real World Applications
publication date: 2010-01-12T00:00:00Z
review text: The authors consider the impulsive Dirichlet boundary value problem \[ \begin{aligned} &-u''(t) + \lambda u(t) = f(t,u(t)) + p(t), \quad t \in [0,T], \\ &\triangle u'(t_j) = I_j(u(t_j)),\;j = 1,\dots,k, \\ &u(0) = u(T) = 0, \end{aligned} \] where \(0 < t_1 < \dots < t_k < T\) are impulse instants, the impulsive functions \(I_j : {\mathbb R} \to {\mathbb R}\) and the right-hand side \(f\) are continuous, \(p \in L^2[0,T]\), \(\lambda > -\pi^2/T^2\). Sufficient conditions for the existence of at least one and infinitely many weak solutions are found. The proofs are based on the critical points theory.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 5656638
zbMATH Keywords: impulsive
zbMATH Keywords: critical points theory
zbMATH Keywords: Dirichlet boundary conditions
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2008.10.044
OpenAlex ID: W2006458524
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DOI: 10.1016/J.NONRWA.2008.10.044
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description: scientific article; zbMATH DE number 5656638