In this paper,we study the following coupled nonlinear logarithmic Hartree system{-Δu+λ_(1)u=μ_(1)(-1/2πln|x|*u^(2))u+β(-1/2πln|x|*v^(2))u,x∈R^(2),-Δv+λ_(2)v=μ_(2)(-1/2πln|x|*v^(2))v+β(-1/2πln|x|*u^(2))v,...In this paper,we study the following coupled nonlinear logarithmic Hartree system{-Δu+λ_(1)u=μ_(1)(-1/2πln|x|*u^(2))u+β(-1/2πln|x|*v^(2))u,x∈R^(2),-Δv+λ_(2)v=μ_(2)(-1/2πln|x|*v^(2))v+β(-1/2πln|x|*u^(2))v,x∈R^(2),where β,μ_(i),λ_(i)(i=1,2)are positive constants,* denotes the convolution in 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.展开更多
基金partially supported by the Natural Science Foundation of China(Grant No.12061012)the special foundation for Guangxi Ba Gui Scholars.
文摘In this paper,we study the following coupled nonlinear logarithmic Hartree system{-Δu+λ_(1)u=μ_(1)(-1/2πln|x|*u^(2))u+β(-1/2πln|x|*v^(2))u,x∈R^(2),-Δv+λ_(2)v=μ_(2)(-1/2πln|x|*v^(2))v+β(-1/2πln|x|*u^(2))v,x∈R^(2),where β,μ_(i),λ_(i)(i=1,2)are positive constants,* denotes the convolution in 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.
