Back to Search
Start Over
Ground states of a Kirchhoff equation with the potential on the lattice graphs
- Source :
- Communications in Analysis and Mechanics, Vol 15, Iss 4, Pp 792-810 (2023)
- Publication Year :
- 2023
- Publisher :
- AIMS Press, 2023.
-
Abstract
- In this paper, we study the nonlinear Kirchhoff equation $ \begin{align*} -\Big(a+b\int_{\mathbb{Z}^{3}}|\nabla u|^{2} d \mu\Big)\Delta u+V(x)u = f(u) \end{align*} $ on lattice graph $ \mathbb{Z}^3 $, where $ a, b > 0 $ are constants and $ V:\mathbb{Z}^{3}\rightarrow \mathbb{R} $ is a positive function. Under a Nehari-type condition and 4-superlinearity condition on $ f $, we use the Nehari method to prove the existence of ground-state solutions to the above equation when $ V $ is coercive. Moreover, we extend the result to noncompact cases in which $ V $ is a periodic function or a bounded potential well.
Details
- Language :
- English
- ISSN :
- 28363310
- Volume :
- 15
- Issue :
- 4
- Database :
- Directory of Open Access Journals
- Journal :
- Communications in Analysis and Mechanics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.570c3a00f4c04274b689b332c72c0d81
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/cam.2023038?viewType=HTML