Multiple unbounded positive solutions for three-point BVPs with sign-changing nonlinearities on the positive half-line
type: Item
instance of: scholarly article
title: Multiple unbounded positive solutions for three-point BVPs with sign-changing nonlinearities on the positive half-line
zbMATH Open document ID: 1195.34042
author: Karima Mebarki
author: Smail Djebali
published in: Acta Applicandae Mathematicae
publication date: 2010-04-23T00:00:00Z
review text: The authors consider the following second-order nonlinear three-point boundary value problem on the positive half-line \[ -x''+cx'+\lambda x=f(t,x(t), x'(t)), \quad t\in (0,\infty), \] \[ x(0)-\alpha x(\eta)=a_0, \quad \lim_{t\to \infty}\frac{x'(t)}{re^{rt}}=b_0, \] where \(a_0, b_0\) are nonnegative real numbers, \(\alpha\geq 0,\) \(\eta>0,\) \(c,\lambda\) are real positive constants, \(r\in (0,c),\) and \(f: (0,\infty)\times [0,\infty)\times {\mathbb R}\to {\mathbb R}\) is a Carathéodory function which may change sign. Under general polynomial growth conditions on \(f\) the existence of nontrivial single and multiple unbounded positive solutions is proved via fixed point theorems in a cone in a special weighted Banach space.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5700594
zbMATH Keywords: Three points BVPs
zbMATH Keywords: positive solutions
zbMATH Keywords: sign-changing nonlinearity
zbMATH Keywords: fixed point
zbMATH Keywords: multiplicity
zbMATH Keywords: cone
MaRDI profile type: Publication
full work available at URL: s10440-008-9322-3
OpenAlex ID: W2003585297
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DOI: 10.1007/S10440-008-9322-3
description: scientific article; zbMATH DE number 5700594