Year: 2024
Author: Biyun Tang, Yongyi Lan
Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 4 : pp. 377–401
Abstract
We investigate the Kirchhoff type elliptic problem $$\Bigg(a+b\int_{\mathbb{R}^N}[|\nabla u|^2+V(x)u^2]dx\Bigg)[-\Delta u+V(x)u]=f(x,u), \ \ \ x\in \mathbb{R}^N,$$where both $V$ and $f$ are periodic in $x,$ 0 belongs to a spectral gap of $−∆+V.$ Under suitable assumptions on $V$ and $f$ with more general conditions, we prove the existence of ground state solutions and infinitely many geometrically distinct solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v37.n4.2
Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 4 : pp. 377–401
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Kirchhoff equation Nehari-Pankov manifold ground state solution multiplicity of solutions.