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Volume 38, Issue 1
Ground State Solutions to a Coupled Nonlinear Logarithmic Hartree System

Qihan He, Yafei Li & Yanfang Peng

DOI: 10.4208/jpde.v38.n1.4

J. Part. Diff. Eq., 38 (2025), pp. 61-79.

Published online: 2025-04

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  • Abstract

In this paper, we study the following coupled nonlinear logarithmic Hartree system

image.png

where $β,\mu_i,λ_i$ ($i=1,2$) are positive constants, ∗ denotes the convolution in $\mathbb{R}^2.$ By considering the constraint minimum problem on the Nehari manifold, we prove the existence of ground state solutions for $β > 0$ large enough. Moreover, we also show that every positive solution is radially symmetric and decays exponentially.

  • Keywords

Hartree system, Logarithmic convolution potential, ground state solution, radial symmetry.

  • AMS Subject Headings

35A01, 35B09, 35J05, 35J47, 35J50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-38-61, author = {He , QihanLi , Yafei and Peng , Yanfang}, title = {Ground State Solutions to a Coupled Nonlinear Logarithmic Hartree System}, journal = {Journal of Partial Differential Equations}, year = {2025}, volume = {38}, number = {1}, pages = {61--79}, abstract = {

In this paper, we study the following coupled nonlinear logarithmic Hartree system

image.png

where $β,\mu_i,λ_i$ ($i=1,2$) are positive constants, ∗ denotes the convolution in $\mathbb{R}^2.$ By considering the constraint minimum problem on the Nehari manifold, we prove the existence of ground state solutions for $β > 0$ large enough. Moreover, we also show that every positive solution is radially symmetric and decays exponentially.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v38.n1.4}, url = {http://global-sci.org/intro/article_detail/jpde/23952.html} }
TY - JOUR T1 - Ground State Solutions to a Coupled Nonlinear Logarithmic Hartree System AU - He , Qihan AU - Li , Yafei AU - Peng , Yanfang JO - Journal of Partial Differential Equations VL - 1 SP - 61 EP - 79 PY - 2025 DA - 2025/04 SN - 38 DO - http://doi.org/10.4208/jpde.v38.n1.4 UR - https://global-sci.org/intro/article_detail/jpde/23952.html KW - Hartree system, Logarithmic convolution potential, ground state solution, radial symmetry. AB -

In this paper, we study the following coupled nonlinear logarithmic Hartree system

image.png

where $β,\mu_i,λ_i$ ($i=1,2$) are positive constants, ∗ denotes the convolution in $\mathbb{R}^2.$ By considering the constraint minimum problem on the Nehari manifold, we prove the existence of ground state solutions for $β > 0$ large enough. Moreover, we also show that every positive solution is radially symmetric and decays exponentially.

He , QihanLi , Yafei and Peng , Yanfang. (2025). Ground State Solutions to a Coupled Nonlinear Logarithmic Hartree System. Journal of Partial Differential Equations. 38 (1). 61-79. doi:10.4208/jpde.v38.n1.4
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