# 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
 [1] Peng Luo. Comparison theorem for diagonally quadratic BSDEs. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020374 [2] Mehdi Bastani, Davod Khojasteh Salkuyeh. On the GSOR iteration method for image restoration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 27-43. doi: 10.3934/naco.2020013 [3] Thierry Horsin, Mohamed Ali Jendoubi. On the convergence to equilibria of a sequence defined by an implicit scheme. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020465 [4] Fabio Camilli, Giulia Cavagnari, Raul De Maio, Benedetto Piccoli. Superposition principle and schemes for measure differential equations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020050 [5] Giuseppina Guatteri, Federica Masiero. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020048 [6] Parikshit Upadhyaya, Elias Jarlebring, Emanuel H. Rubensson. A density matrix approach to the convergence of the self-consistent field iteration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 99-115. doi: 10.3934/naco.2020018

2019 Impact Factor: 1.105