Existence of semilinear elliptic equations with prescribed limiting behaviour | Zendy

Ibrahim Hassan | Zendy; Nasreddine Elissar | Zendy

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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.

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