Variational method to the impulsive equation with Neumann boundary conditions
type: Item
instance of: scholarly article
title: Variational method to the impulsive equation with Neumann boundary conditions
zbMATH Open document ID: 1184.34039
DOI: 10.1155/2009/316812
author: Juntao Sun
author: Haibo Chen
published in: Boundary Value Problems
publication date: 2009-11-06T00:00:00Z
full work available at URL: https://eudml.org/doc/45604
review text: The authors consider the impulsive boundary value problem \[ \begin{aligned} -(p(t)u'(t))' + r(t)u'(t) + q(t)u(t) &= g(t,u(t)),\quad \text{a.e. } t \in [0,1],\;t \neq t_k, \\ -\triangle(p(t_k)u'(t_k)) &= I_k(u(t_k)),\quad k = 1,\ldots,p-1,\\ u'(0+) &= u'(1-) = 0, \end{aligned} \] where \(0 < t_1 < \ldots < t_{p-1} < 1\); \(p \in C^1([0,1])\), \(r\), \(q \in C([0,1])\), \(g\), \(I_k\) are continuous functions. Sufficient conditions for the existence of at least one (two, infinitely many) solutions are obtained by using a variational approach and critical point theorems.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 5626150
zbMATH Keywords: impulsive boundary value problem
zbMATH Keywords: second order
zbMATH Keywords: Neumann boundary conditions
zbMATH Keywords: variational methods
zbMATH Keywords: existence of solution
zbMATH Keywords: critical point theory
Wikidata QID: Q59219996
MaRDI profile type: Publication
OpenAlex ID: W2005958549
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description: scientific article; zbMATH DE number 5626150