Positive solutions for a nonhomogeneous Kirchhoff equation with the asymptotical nonlinearity in \(R^3\)
type: Item
instance of: scholarly article
title: Positive solutions for a nonhomogeneous Kirchhoff equation with the asymptotical nonlinearity in \(R^3\)
zbMATH Open document ID: 1474.35298
DOI: 10.1155/2014/710949
author: Ling Ding
author: L. Li
author: J. L. Zhang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We study the following nonhomogeneous Kirchhoff equation: \(-(a + b \int_{R^3} | \nabla u |^2 d x) \Delta u + u = k(x) f(u) + h(x)\), \(x \in R^3\), \(u \in H^1(R^3)\), \(u > 0\), \(x \in R^3\), where \(f\) is asymptotically linear with respect to \(t\) at infinity. Under appropriate assumptions on \(k, f\), and \(h\), existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 7022928
Wikidata QID: Q59040824
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/710949
OpenAlex ID: W2057159959
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description: scientific article; zbMATH DE number 7022928