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Ground State Solutions for Kirchhoff Equations via Modified Nehari-Pankov Manifold

Ground State Solutions for Kirchhoff Equations via Modified Nehari-Pankov Manifold

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.

Author Details

Biyun Tang

Yongyi Lan