5 papers
Bound state solutions for non-autonomous fractional Schrödinger-Poisson equations with critical exponent
Kexue Li
In this paper, we study the fractional Schrödinger-Poisson equation \begin{equation*} \ \left\{\begin{aligned} &(-Δ)^{s}u+V(x)u+K(x)ϕu=|u|^{2^{\ast}_{s}-2}u, &\mbox{in} \ \mathbb{R…
Fractional elliptic equations with Hardy potential and critical nonlinearities
Kexue Li
In this paper, we consider the fractional elliptic equation \begin{align*} \left\{\begin{aligned} &(-Δ)^s u-μ\frac{u}{|x|^{2s}} = \frac{|u|^{2_s^\ast (α)-2}u}{|x|^α} + f(x,u), && \…
No local solutions for semilinear fractional heat equations
Kexue Li
We study the Cauchy problem for the semilinear fractional heat equation with non-negative initial value and locally L…
A characteristic of local existence for fractional heat equations in Lebesgue spaces
Kexue Li
In this paper, we consider the fractional heat equation with Dirichlet boundary conditions on the ball , where $\triangle…
Maximum principles for a time-space fractional diffusion equation
Junxiong Jia, Kexue Li
In this paper, we focus on maximum principles of a time-space fractional diffusion equation. Maximum principles for classical solution and weak solution are all obtained by using p…