Nonlocal Problems at Nearly Critical Growth
نویسنده
چکیده
We study the asymptotic behavior of solutions to the nonlocal nonlinear equation (−∆p) u = |u|u in a bounded domain Ω ⊂ R as q approaches the critical Sobolev exponent 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 = 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.
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