Properties of positive harmonic functions on the half-space with a nonlinear boundary condition
- Abreu, Emerson
- do Ó, João Marcos
- Medeiros, Everaldo
Publication date
February 2010
DOI Publisher
Elsevier Inc. ISSN
0022-0396 Citation count (estimate)
7Abstract
AbstractIn this paper we study existence and properties of solutions of the problem Δw=0 on the half-space R+N with nonlinear boundary condition ∂w/∂η+w=|w|p−2w where 2<p<2(N−1)/(N−2) and N⩾3. We obtain a ground state solution w=w(x1,…,xN−1,t) which is radial and has exponential decay in the first N−1 variables. Moreover, w has sharp polynomial decay in the variable t
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