Positive solutions of a nonlinear fourth-order dynamic eigenvalue problem on time scales
type: Item
instance of: scholarly article
title: Positive solutions of a nonlinear fourth-order dynamic eigenvalue problem on time scales
zbMATH Open document ID: 1242.34157
DOI: 10.1155/2012/798796
author: Hua Luo
author: Chenghua Gao
published in: Abstract and Applied Analysis
publication date: 2012-07-18T00:00:00Z
review text: Summary: Let \(\mathbb T\) be a time scale and \(a, b \in \mathbb T, a < \rho^2(b)\). We study the nonlinear fourth-order eigenvalue problem on \(\mathbb T, u^{\Delta^4}(t) = \lambda h(t)f(u(t), u^{\Delta^2}(t)), t \in [a, \rho^2(b)]_{\mathbb T}, u(a) = u^\Delta(\sigma(b)) = u^{\Delta^2}(a) = u^{\Delta^3}(\rho(b)) = 0\) and obtain the existence and nonexistence of positive solutions when \(0 < \lambda \leq \lambda^\ast\) and \(\lambda > \lambda^\ast\), respectively,for some \(\lambda^\ast\). The main tools to prove the existence results are the Schauder fixed point theorem and the upper and lower solution method.
Mathematics Subject Classification ID: 34N05
zbMATH DE Number: 6058161
Wikidata QID: Q58696817
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/798796
OpenAlex ID: W2009720048
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description: scientific article; zbMATH DE number 6058161