Positive solutions for singular impulsive Dirichlet boundary value problems
type: Item
instance of: scholarly article
title: Positive solutions for singular impulsive Dirichlet boundary value problems
zbMATH Open document ID: 1427.34041
DOI: 10.12775/TMNA.2018.017
author: Liang Bai
author: Juan J. Nieto
published in: Topological Methods in Nonlinear Analysis
publication date: 2019-05-07T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.tmna/1541473236
review text: The authors present sufficient conditions for the existence of one or two positive classical solutions for the following singular Dirichlet boundary value problem \[ \begin{gathered} -u''(t)-\frac{1}{u^\alpha(t)}= \lambda f (t, u(t)), \quad t \in \Omega,\\ u'(t_i^+)-u'(t^-_i)=I_i(u(t_i)), \quad i=1,\dots, p,\\ u(0)=u(1)=0 \end{gathered} \] where \(\lambda \in (0,+\infty)\), \(\alpha \in (0,1)\), \(\Omega = (0,1)\setminus \{t_1,\dots, t_p\}\), \(0=t_0<t_1< \dots < t_p < t_{p+1}=1\), \(f\in C([0,1]\times [0,+\infty);[0,+\infty))\) and \(I_i \in C([0,\infty);(-\infty,0])\) for each \(i=1,\dots,p\). The results are obtained by using a variational method and critical point theory.
reviewed by: Daniel Franco
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 58E50
zbMATH DE Number: 7051680
zbMATH Keywords: singular differential equations
zbMATH Keywords: impulses
zbMATH Keywords: critical points
zbMATH Keywords: mountain pass lemma
MaRDI profile type: Publication
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OpenAlex ID: W2899981792
description: scientific article; zbMATH DE number 7051680