3 papers
math.FA2026
Some Reverse Hardy-Littlewood-Sobolev Type Inequalities
Qianqiao Guo, Zhe Pu, Jiankang Xia
We establish some sharp reverse Hardy-Littlewood-Sobolev (HLS) type inequalities on \(\mathbb{R}^n\) and \(\mathbb{R}_+^n\). Using an operator representation, we overcome the diffi…
math.AP2026
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…
math.AP2021
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…