# American Institute of Mathematical Sciences

March  2005, 4(1): 93-99. doi: 10.3934/cpaa.2005.4.93

## Gamma-star-shapedness for semilinear elliptic equations

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

Received  February 2004 Revised  November 2004 Published  December 2004

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.
Citation: Antonio Greco, Marcello Lucia. Gamma-star-shapedness for semilinear elliptic equations. Communications on Pure & Applied Analysis, 2005, 4 (1) : 93-99. doi: 10.3934/cpaa.2005.4.93
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