Two nontrivial solutions for the nonhomogenous fourth order Kirchhoff equation
type: Item
instance of: scholarly article
title: Two nontrivial solutions for the nonhomogenous fourth order Kirchhoff equation
zbMATH Open document ID: 1372.35097
DOI: 10.4171/ZAA/1585
author: Ling Ding
author: L. Li
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2017-05-16T00:00:00Z
review text: Summary: In this paper, we consider the following nonhomogenous fourth order Kirchhoff equation \[ \Delta^2 u - \left( a + b \int_{\mathbb{R}^N} |\nabla u|^2 dx \right) \Delta u + V(x) u = f(x,u) + g(x),\quad x\in \mathbb{R}^N, \] where \(\Delta^2 := \Delta(\Delta)\), constants \(a > 0\), \(b \geq 0\), \(V \in C(\mathbb{R}^N\), \(\mathbb{R})\), \(f \in C(\mathbb{R}^N \times \mathbb{R}, \mathbb{R})\) and \(g \in L^2(\mathbb{R}^N)\). Under more relaxed assumptions on the nonlinear term \(f\) that are much weaker than those in L. Xu and H. Chen, using some new proof techniques especially the verification of the boundedness of Palais-Smale sequence, a new result is obtained.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J35
zbMATH DE Number: 6718158
zbMATH Keywords: fourth order Kirchhoff equation
zbMATH Keywords: variational methods
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6718158