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A Nonlinear Dirichlet Problem on the Unit Ball
Author(s) -
Rother Wolfgang
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211600108
Subject(s) - mathematics , unit sphere , dirichlet problem , ball (mathematics) , nonlinear system , dirichlet's energy , dirichlet distribution , mathematical analysis , dirichlet's principle , pure mathematics , boundary value problem , physics , quantum mechanics
In the present paper, we consider the nonlinear Dirichlet problem ‐ Δ u ( x ) u β ( x ) = 0is the unit ball and q is a continuous radially symmetric function on B which may be singular on ∂B. We state some mild conditions for the function q so that the Dirichlet problem has a positive classical solution.