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

Author

Listed:
  • Khadijah Abdullah Sharaf

    (King Abdulaziz University)

  • Hichem Chtioui

    (Faculty of Sciences of Sfax)

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.

Suggested Citation

  • Khadijah Abdullah Sharaf & Hichem Chtioui, 2020. "The topological contribution of the critical points at infinity for critical fractional Yamabe-type equations," Partial Differential Equations and Applications, Springer, vol. 1(3), pages 1-26, June.
    • Handle: RePEc:spr:pardea:v:1:y:2020:i:3:d:10.1007_s42985-020-00011-5
    DOI: 10.1007/s42985-020-00011-5
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