TY - JOUR
T1 - Ground State Solutions for Kirchhoff Equations via Modified Nehari-Pankov Manifold
AU - Tang , Biyun
AU - Lan , Yongyi
JO - Journal of Partial Differential Equations
VL - 4
SP - 377
EP - 401
PY - 2024
DA - 2024/12
SN - 37
DO - http://doi.org/10.4208/jpde.v37.n4.2
UR - https://global-sci.org/intro/article_detail/jpde/23687.html
KW - Kirchhoff equation, Nehari-Pankov manifold, ground state solution, multiplicity of solutions.
AB - <p style="text-align: justify;">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.</p>