64 citations · 152 across the 7 of their papers we have counts for
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Positive solutions to the nonlinear Choquard equation: symmetry, uniqueness, and nondegeneracy
Jiankang Xia, Chengxiang Zhang, Xu Zhang
We study the symmetry, uniqueness, and nondegeneracy of positive solutions to the Choquard equation in , which have long remained open proble…
Normalized groundstates for mixed -Laplacian equations in with exponential critical growth
Jiankang Xia, Chao Zhong
We investigate normalized groundstates for mixed -Laplacian equations \begin{align*} \begin{cases} -Δ_p u-Δu+λu=f(u) & \text{in } \mathbb{R}^2, \displaystyle \int_{\mathbb{R…
Saddle solutions for the Choquard equation with a general nonlinearity
Jiankang Xia
In the spirit of Berestycki and Lions, we prove the existence of saddle type nodal solutions for the Choquard equation \[ -Δu + u= \big(I_α\ast F(u)\big)F'(u)\qquad \text{ in }\;\m…
Saddle solutions for the fractional Choquard equation
Yin-Xin Cui, Jiankang Xia
We study the saddle solutions for the fractional Choquard equation \begin{align*} (-Δ)^{s}u+ u=(K_α\ast|u|^{p})|u|^{p-2}u, \quad x\in \mathbb{R}^N \end{align*} where , $…
Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent
Jean Van Schaftingen, Jiankang Xia
We prove the existence of ground state solutions by variational methods to the nonlinear Choquard equations with a nonlinear perturbation \[ -Δu+ u=\big(I_α*|u|^{\fracα{N}+1}\big)|…
Standing waves with a critical frequency for nonlinear Choquard equations
Jean Van Schaftingen, Jiankang Xia
In this paper, we study the nonlocal Choquard equation where $N\ge…
Choquard equations under confining external potentials
Jean Van Schaftingen, Jiankang Xia
We consider the nonlinear Choquard equation where , is the Riesz potentia…