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math.AP2024★ 2 cited
Variational method for fractional Hamiltonian system in bounded domain
Weimin Zhang
Here we consider the following fractional Hamiltonian system \begin{equation*} \begin{cases} \begin{aligned} (-Δ)^{s} u&=H_v(u,v) \;\;&&\text{in}~Ω,\\ (-Δ)^{s} v&=H_u(u,v) &&\text{…
math.AP2024
Stable solution and extremal solution for fractional -Laplacian
Weimin Zhang
To our knowledge, this paper is the first attempt to consider the existence issue for fractional -Laplacian equation: $(-Δ)_p^s u= λf(u),\; u> 0 ~\text{in}~Ω;\; u=0\;\text{in}~…