Open AccessGamma-star-shapedness for semilinear elliptic equations
Author(s) -
Antonio Greco,
Marcello Lucia
Publication year - 2005
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2005.4.93
Subject(s) - bounded function , star (game theory) , elliptic curve , mathematical analysis , mathematics , product (mathematics) , physics , property (philosophy) , power (physics) , boundary value problem , pure mathematics , boundary (topology) , geometry , thermodynamics , philosophy , epistemology
A generic semilinear equation in a star-shaped ring is considered. Any solution bounded between its boundary values is shown to be decreasing along rays starting from the origin, provided that a structural condition is satisfied. A corresponding property for the product between the solution and a (positive) power of |x| is also investigated. Applications to the Emden-Fowler and the Liouville equation are developed.\u