Gamma-star-shapedness for semilinear elliptic equations

Antonio Greco; Marcello Lucia

doi:10.3934/cpaa.2005.4.93

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2005, Volume 4, Issue 1: 93-99. Doi: 10.3934/cpaa.2005.4.93

This issue Previous Article Maximal function estimates with applications to a modified Kadomstev-Petviashvili equation Next Article The Faber--Krahn inequality for random/nonautonomous parabolic equations

Gamma-star-shapedness for semilinear elliptic equations

Antonio Greco^1, and
Marcello Lucia^2,

1.
Dipartimento di Matematica, Università di Cagliari, via Ospedale 72, 09124 Cagliari
2.
Dept. Math. - Hill Center, Rutgers University, 110 Frelinghuysen Rd, Piscataway NJ 08854

Received: January 31, 2004

Revised: October 31, 2004

Published: February 2005

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

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