Existence of positive solutions of one-dimensional prescribed mean curvature equation
type: Item
instance of: scholarly article
title: Existence of positive solutions of one-dimensional prescribed mean curvature equation
zbMATH Open document ID: 1407.34040
DOI: 10.1155/2014/610926
author: Lingfang Jiang
author: Ruyun Ma
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: We consider the existence of positive solutions of one-dimensional prescribed mean curvature equation \(-(u' / \sqrt{1 + u^{\prime 2}})' = \lambda f(u)\), \(0 < t < 1\), \(u(t) > 0\), \(t \in(0, 1)\), \(u(0) = u(1) = 0\) where \(\lambda > 0\) is a parameter, and \(f : [0, \infty) \rightarrow [0, \infty)\) is continuous. Further, when \(f\) satisfies \(\max \{u^p, u^q \} \leq f(u) \leq u^p + u^q\), \(0 < p \leq q < + \infty\), we obtain the exact number of positive solutions. The main results are based upon quadrature method.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B08
zbMATH DE Number: 7016859
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/610926
OpenAlex ID: W1966230200
Wikidata QID: Q59066555
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description: scientific article; zbMATH DE number 7016859