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Volume 37, Issue 4
Ground State Solutions for Kirchhoff Equations via Modified Nehari-Pankov Manifold

Biyun Tang & Yongyi Lan

DOI: 10.4208/jpde.v37.n4.2

J. Part. Diff. Eq., 37 (2024), pp. 377-401.

Published online: 2024-12

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  • 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.

  • Keywords

Kirchhoff equation, Nehari-Pankov manifold, ground state solution, multiplicity of solutions.

  • AMS Subject Headings

35J35, 35B38, 35J92

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JPDE-37-377, author = {Tang , Biyun and Lan , Yongyi}, title = {Ground State Solutions for Kirchhoff Equations via Modified Nehari-Pankov Manifold}, journal = {Journal of Partial Differential Equations}, year = {2024}, volume = {37}, number = {4}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v37.n4.2}, url = {http://global-sci.org/intro/article_detail/jpde/23687.html} }
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 -

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.

Tang , Biyun and Lan , Yongyi. (2024). Ground State Solutions for Kirchhoff Equations via Modified Nehari-Pankov Manifold. Journal of Partial Differential Equations. 37 (4). 377-401. doi:10.4208/jpde.v37.n4.2
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