[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