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Gamma-star-shapedness for semilinear elliptic equations

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  • 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.
    Mathematics Subject Classification: 35J65, 35B30, 35A30, 52A30.


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