Positive solutions of nonlinear problems at resonance
type: Item
instance of: scholarly article
title: Positive solutions of nonlinear problems at resonance
zbMATH Open document ID: 0811.47061
DOI: 10.1007/BF00050896
published in: Acta Mathematica Hungarica
publication date: 1993-04-01T00:00:00Z
review text: This article deals with the semilinear problem of the form \[ Lu= Nu, \] where \(L: D(L)\subset \mathbb{E}\to \mathbb{F}\) is a noninvertible linear operator, \(N: \mathbb{E}\to \mathbb{F}\) is a nonlinear operator, \(\mathbb{E}\) and \(\mathbb{F}\) are Banach spaces. An existence theorem in a cone which improved some earlier results of the author and the existence of a positive periodic solution of the equation \[ u''+ u+ \mu u^ 2= \varepsilon\cos \omega t \] using the method of upper and lower solution are proved.
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 148679
zbMATH Keywords: method of upper and lower solution
zbMATH Keywords: semilinear problem
zbMATH Keywords: noninvertible linear operator
zbMATH Keywords: nonlinear operator
zbMATH Keywords: existence of a positive periodic solution
author: Juan J. Nieto
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
Wikidata QID: Q60199487
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description: scientific article; zbMATH DE number 148679