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.
Gamma-star-shapedness for semilinear elliptic equations
GRECO, ANTONIO;
2005-01-01
Abstract
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.
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