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Tingxi Hu

Publications and source records attributed to Tingxi Hu.

4 recordsLinked to original sources
arXiv2017

Existence and asymptotic behavior of the least energy solutions for fractional Choquard equations with potential well

In this paper, we are concerned with the existence and asymptotic behavior of least energy solutions for following nonlinear Choquard equation driven by fractional Laplacian $$(-Δ)^{s} u+λV(x)u=(I_α\ast F(u))f(u) \ \ in \ \ R^{N},$$ where $N> 2s$, $ (N-4s)^{+}<α< N$, $λ$ is a positive parameter and the nonnegative potential function $V(x)$ is continuous. By variational methods, we prove the existence of least energy solution which localize near the potential well $int (V^{-1}(0))$ as $λ$ large enough.

math.AP↗
arXiv2014

Schauder estimates for solutions of sub-Laplace equations with Dini terms

In this paper we establish Schauder estimates for the sublalpace equation \[Σ_{j = 1}^mX_j^2u = f,\] where ${X_1},{X_2}, \ldots ,{X_m}$ is a system of smooth vector field which generates the first layer in the Lie algebra of a Carnot group. We drive the estimate for the second order derivatives of the solution to the equation with Dini continue inhomogeneous term $f$ by the perturbation argument.

math.AP↗
arXiv2014

Existence of optimizers of the Stein-Weiss inequalities on Carnot groups

This paper proves existence of optimizers of the Stein-Weiss inequalities on Carnot groups under some conditions. The adjustment of Lions' concentration compactness principles to Carnot groups plays an important role in our proof. Unlike known treatment to the Hardy-Littlewood-Sobolev inequality on Heisenberg group, our arguments relate to the powers of the weight functions.

math.FA↗