Impulsive boundary value problems with integral boundary conditions and one-dimensional \(p\)-Laplacian
type: Item
instance of: scholarly article
title: Impulsive boundary value problems with integral boundary conditions and one-dimensional \(p\)-Laplacian
zbMATH Open document ID: 1169.34022
author: Bo Du
author: Weigao Ge
author: Meiqiang Feng
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-04-02T00:00:00Z
review text: The authors consider the impulsive boundary value problem of second order with \(p\)-Laplacian \[ \begin{aligned} &-(\varphi_p(u'(t)))' = f(t,u(t)),\quad t \in (0,1)\setminus\{t_1,\dots,t_m\},\\ &-\triangle u|_{t=t_k} = I_k(u(t_k)), \quad k = 1,\dots,m,\\ &u'(0) = 0, \quad u(1) = \int_0^1 g(t)u(t) \,dt, \end{aligned} \] where \(0 < t_1 < \dots < t_m < 1\) are impulse points, \(f\), \(I_k\) are continuous, \(g\) is integrable on \([0,1]\) and nonnegative. Sufficient conditions ensuring the existence of at least two positive solutions of the BVP are obtained. The proofs are based on fixed point theorem in cones.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 5539191
zbMATH Keywords: boundary value problem
zbMATH Keywords: impulses
zbMATH Keywords: positive solutions
zbMATH Keywords: fixed point theorem
zbMATH Keywords: multiplicity result
zbMATH Keywords: \(p\)-Laplacian
MaRDI profile type: Publication
full work available at URL: j.na.2008.04.015
OpenAlex ID: W1990556541
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DOI: 10.1016/J.NA.2008.04.015
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description: scientific article; zbMATH DE number 5539191