Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
839347 | Nonlinear Analysis: Theory, Methods & Applications | 2016 | 18 Pages |
Abstract
We study the asymptotic behavior of solutions to the nonlocal nonlinear equation (−Δp)su=|u|q−2u(−Δp)su=|u|q−2u in a bounded domain Ω⊂RNΩ⊂RN as qq approaches the critical Sobolev exponent p∗=Np/(N−ps)p∗=Np/(N−ps). We prove that ground state solutions concentrate at a single point x̄∈Ω¯ and analyze the asymptotic behavior for sequences of solutions at higher energy levels. In the semi-linear case p=2p=2, we prove that for smooth domains the concentration point x̄ cannot lie on the boundary, and identify its location in the case of annular domains.
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Engineering (General)
Authors
Sunra Mosconi, Marco Squassina,