In this paper we deal with non coercive elliptic systems of divergence type, that include both the $p$-Laplacian and the mean curvature operator and whose right hand sides depend also on a gradient factor. We prove that any nonnegative entire (weak) solution is necessarily constant. The main argument of our proofs is based on previous estimates, given in a previous paper for elliptic inequalities. Actually, the main technique for proving the central estimate has been developed by Mitidieri and Pohozaev and relies on the method of test functions. No use of comparison and maximum principles or assumptions on symmetry or behavior at infinity of the solutions are required.
Nonexistence of nonnegative solutions of elliptic systems of divergence type.
FILIPPUCCI, Roberta
2011
Abstract
In this paper we deal with non coercive elliptic systems of divergence type, that include both the $p$-Laplacian and the mean curvature operator and whose right hand sides depend also on a gradient factor. We prove that any nonnegative entire (weak) solution is necessarily constant. The main argument of our proofs is based on previous estimates, given in a previous paper for elliptic inequalities. Actually, the main technique for proving the central estimate has been developed by Mitidieri and Pohozaev and relies on the method of test functions. No use of comparison and maximum principles or assumptions on symmetry or behavior at infinity of the solutions are required.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
