[Author]
 Ustinov, Nikita S.

[Title]
 On solvability of a critical semilinear problem with the spectral Neumann
 fractional Laplacian

[AMS Subj-class]
 35R11 Fractional partial differential equations
 35A01 Existence problems for PDEs: global existence, local existence, non-existence

[Abstract]
 We provide the sufficient conditions for the existence of the ground state solution
 for the problem generated by the fractional Sobolev inequality in
 $\Omega \in C^1:$ $(-\Delta)_{Sp}^s u(x) + u(x) = u^{2^*_s-1}(x)$.  Here 
 $(-\Delta)_{Sp}^s$ stands for the $s$-th power of the conventional Neumann
 Laplacian in $\Omega \Subset \mathbb{R}^n$, $n \geq 3$, 
 $s \in (0, 1)$, $2^*_{s} = 2n/(n-2s)$. For the local case $s = 1$ corresponding
 results were obtained earlier for the Neumann Laplacian and Neumann $p$-Laplacian
 operators.

[Comments]
 LaTeX, Russian, 15 pp.

[Contact e-mail]
 ustinns@yandex.ru