On the existence of solutions to one-dimensional fourth-order equations
type: Item
instance of: scholarly article
title: On the existence of solutions to one-dimensional fourth-order equations
zbMATH Open document ID: 1472.49004
author: Armin Hadjian
author: S. Shokooh
author: Ghasem A. Afrouzi
published in: Ukrainian Mathematical Journal
publication date: 2021-06-21T00:00:00Z
review text: In this paper, the authors consider the following fourth-order boundary-value problem: \begin{align*} & u^{(4)}h(x,u')-u''=[\lambda f(x,u)+g(u)]h(x,u')\ in\ ]0, 1[\\ & u(0)=u(1)=0=u''(0)=u''(1), \tag{1}\end{align*} where \(\lambda\) is a positive parameter, \(f:[0, 1]\times\mathbb{R}\longrightarrow\mathbb{R}\) is an \(L^{1}-\)Caratheodory function, \(g:\mathbb{R}\longrightarrow\mathbb{R}\) is a Lipschitz continuous function and \(h:[0, 1]\times\mathbb{R}\longrightarrow [0,\infty[\) is a bounded and continuous function. Using variational methods and Ricceri's variational principle, they prove under suitable conditions on \(\lambda,f,g,h\) that problem (1) admits at least one nontrivial weak solution.
reviewed by: Mohsen Timoumi
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 7361391
zbMATH Keywords: fourth-order differential equations, variational methods, critical point theory
MaRDI profile type: Publication
full work available at URL: s11253-021-01891-5
OpenAlex ID: W3110038092
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DOI: 10.1007/S11253-021-01891-5
description: scientific article; zbMATH DE number 7361391