Gamma-star-shapedness for semilinear elliptic equations | Zendy

Antonio Greco | Zendy; Marcello Lucia | Zendy

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Gamma-star-shapedness for semilinear elliptic equations

Author(s) -

Antonio Greco,

Marcello Lucia

Publication year - 2005

Publication title -

communications on pure andamp 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

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