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Existence of semilinear elliptic equations with prescribed limiting behaviour
Author(s) -
Ibrahim Hassan,
Nasreddine Elissar
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3851
Subject(s) - mathematics , limiting , bounded function , dirichlet boundary condition , dirichlet problem , space (punctuation) , dirichlet distribution , mathematical analysis , boundary (topology) , elliptic curve , boundary value problem , pure mathematics , mechanical engineering , linguistics , philosophy , engineering
In this paper, we consider semilinear elliptic equations of the form Δ u + f (u) = 0 over a quarter space with Dirichlet boundary conditions. Given a suitable positive root z of f , we show how to construct a non‐negative bounded solution u converging to a one‐dimensional limiting profile V with V ( ∞ ) = z . This is established using Perron's method by constructing sub‐solutions and super‐solutions and employing a sliding argument. Copyright © 2016 John Wiley & Sons, Ltd.