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 - <p style="text-align: justify;">In this paper, we study the following coupled nonlinear logarithmic Hartree
system<br/></p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20250408/1744100193327310.png" title="1744100193327310.png" alt="image.png"/></p><p style="text-align: justify;">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 $β &gt; 0$ large enough. Moreover, we also show
that every positive solution is radially symmetric and decays exponentially.<br/></p>