20 citations · 69 across the 25 of their papers we have counts for
6 papers · 2 filters
Partial regularity of stable solutions to the fractional Gel'fand-Liouville equation
Ali Hyder, Wen Yang
We analyze stable weak solutions to the fractional Gel'fand problem \begin{equation*} (-Δ)^su=e^u\quad\mathrm{in}\quad Ω\subset\mathbb{R}^n. \end{equation*} We prove that the dimen…
Normal conformal metrics on with -curvature having power-like growth
Ali Hyder, Luca Martinazzi
Answering a question by M. Struwe (Vietnam J. Math. 2020) related to the blow-up behaviour in the Nirenberg problem, we show that the prescribed -curvature equation $$Δ^2 u=(1-|…
Singular Yamabe metrics by equivariant reduction
Ali Hyder, Angela Pistoia, Yannick Sire
We construct singular solutions to the Yamabe equation using a reduction of the problem in an equivariant setting. This provides a non-trivial geometric example for which the analy…
Classification of stable solutions to a non-local Gelfand-Liouville equation
Ali Hyder, Wen Yang
We study finite Morse index solutions to the non-local Gelfand-Liouville problem for every and . Precisely, we…
Concentration phenomena to a higher order Liouville equation
Ali Hyder
We study blow-up and quantization phenomena for a sequence of solutions to the prescribed -curvature problem $$ (-Δ)^nu_k= Q_ke^{2nu_k}\quad \text{in }Ω\subset\mathbb{R}…
Removability of singularities and superharmonicity for some fractional Laplacian equations
Weiwei Ao, Maria del Mar Gonzalez, Ali Hyder +1
We study some qualitative properties (including removable singularities and superharmonicity) of non-negative solutions to whi…