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- W4301677358 abstract "We study the asymptotic behavior of solutions to the nonlocal nonlinear equation $(-Delta_p)^s u=|u|^{q-2}u$ in a bounded domain $Omegasubset{mathbb R}^N$ as $q$ approaches the critical Sobolev exponent $p^*=Np/(N-ps)$. We prove that ground state solutions concentrate at a single point $bar xin overlineOmega$ and analyze the asymptotic behavior for sequences of solutions at higher energy levels. In the semi-linear case $p=2,$ we prove that for smooth domains the concentration point $bar x$ cannot lie on the boundary, and identify its location in the case of annular domains." @default.
- W4301677358 created "2022-10-05" @default.
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- W4301677358 date "2015-12-07" @default.
- W4301677358 modified "2023-09-28" @default.
- W4301677358 title "Nonlocal problems at nearly critical growth" @default.
- W4301677358 doi "https://doi.org/10.48550/arxiv.1512.01956" @default.
- W4301677358 hasPublicationYear "2015" @default.
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