arXiv subjects
Publications and source records attributed to Vicentiu D. Rădulescu.
We consider a Kirchhoff-type diffusion problem driven by the magnetic fractional Laplace operator. The main result in this paper establishes that infinite time blow-up cannot occur for the problem. The proof is based on the potential well method, in relationship with energy and Nehari functionals.
In this paper, we first establish the uniqueness and non-degeneracy of positive solutions to the fractional Kirchhoff problem \begin{equation*} \Big(a+b{\int_{\mathbb{R}^{N}}}|(-Δ)^{\frac{s}{2}}u|^2dx\Big)(-Δ)^su+mu=|u|^{p-2}u,\quad \text{in}\ \mathbb{R}^{N}, \end{equation*} where $a,b,m>0$, $0<\frac{N}{4} 0$ sufficiently small and a potential function $V$.
In this paper, we consider the following singularly perturbed fractional Kirchhoff problem \begin{equation*} \Big(\varepsilon^{2s}a+\varepsilon^{4s-N} b{\int_{\mathbb{R}^{N}}}|(-Δ)^{\frac{s}{2}}u|^2dx\Big)(-Δ)^su+V(x)u=|u|^{p-2}u,\quad \text{in}\ \mathbb{R}^{N}, \end{equation*} where $a,b>0$, $2s 0$ sufficiently small and a bounded continuous function $V$, we establish a type of local Pohozǎev identity by extension technique and then we can obtain the local uniqueness of semiclassical bounded solutions based on our recent results on the uniqueness and non-degeneracy of positive solutions to the limit problem.