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On elliptic equations with N-independent stable operators
Lele Du, Minbo Yang
We investigate the positive solutions of the semilinear elliptic equation \begin{align*} \sum^{N}_{i=1}\left(-\partial_{ii}\right)^{s}u=u^{p} \end{align*} with one-dimensional symm…
Liouville results for semilinear integral equations with conical diffusion
Isabeau Birindelli, Lele Du, Giulio Galise
Nonexistence results for positive supersolutions of the equation are obtained, being any symmetric and stable linear operator, positi…
Positive solutions to the planar logarithmic Choquard equation via asymptotic approximation
Daniele Cassani, Lele Du, Zhisu Liu
In this paper we study the following nonlinear Choquard equation where …
Fine bounds for best constants of fractional subcritical Sobolev embeddings and applications to nonlocal PDEs
Daniele Cassani, Lele Du
We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings \begin{align*} W_{0}^{s,p}\left(Ω\right)\hookrightarrow L^{q}\left(Ω\right), \end{align…
Uniqueness and nondegeneracy of solutions for a critical nonlocal equation
Lele Du, Minbo Yang
The aim of this paper is to classify the positive solutions of the nonlocal critical equation: …
On elliptic equations with Stein-Weiss type convolution parts
Lele Du, Fashun Gao, Minbo Yang
The aim of this paper is to study the critical elliptic equations with Stein-Weiss type convolution parts $$ \displaystyle-Δu =\frac{1}{|x|^α}\left(\int_{\mathbb{R}^{N}}\frac{|u(y)…