The topological contribution of the critical points at infinity for critical fractional Yamabe-type equations

Khadijah Abdullah Sharaf () and Hichem Chtioui ()
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Khadijah Abdullah Sharaf: King Abdulaziz University
Hichem Chtioui: Faculty of Sciences of Sfax

Partial Differential Equations and Applications, 2020, vol. 1, issue 3, 1-26

Abstract: Abstract In this paper, we study the critical fractional nonlinear PDE: $$(-\Delta )^{s}u= u^\frac{n+2s}{n-2s}$$ ( - Δ ) s u = u n + 2 s n - 2 s , $${u>0}$$ u > 0 in $$\Omega $$ Ω and $$u=0$$ u = 0 on $$\partial \Omega $$ ∂ Ω , where $$\Omega $$ Ω is a thin annuli-domain of $${\mathbb{R}}^n, n\ge 2.$$ R n , n ≥ 2 . We compute the evaluation of the difference of topology induced by the critical points at infinity between the level sets of the associated variational function. Our Theorem can be seen as a nonlocal analog of the result of Ahmedou and El Mehdi (Duke Math J 94:215–229, 1998) on the classical Yamabe-type equation.

Keywords: Fractional operator; Calculus of variational; Critical points at infinity; 35J65; 58J20; 58C30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-020-00011-5

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