We study the asymptotic behavior of solutions to the nonlocal nonlinear equation (-Delta(p))(s)u = vertical bar u vertical bar(q-2)u in a bounded domain Omega subset of R-N as q approaches the critical Sobolev exponent p* = Np/(N - ps). We prove that ground state solutions concentrate at a single point (x) over bar epsilon (Omega) over bar 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 (x) over bar cannot lie on the boundary, and identify its location in the case of annular domains

Nonlocal problems at nearly critical growth

MOSCONI, SUNRA JOHANNES NIKOLAJ;
2016

Abstract

We study the asymptotic behavior of solutions to the nonlocal nonlinear equation (-Delta(p))(s)u = vertical bar u vertical bar(q-2)u in a bounded domain Omega subset of R-N as q approaches the critical Sobolev exponent p* = Np/(N - ps). We prove that ground state solutions concentrate at a single point (x) over bar epsilon (Omega) over bar 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 (x) over bar cannot lie on the boundary, and identify its location in the case of annular domains
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/253030
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