The boundary value problem and notation are as in previous paper of Pucci and Serrin [Indiana Univ. Math. J. 47 (1998), no. 2, 501-528]. A uniqueness theorem for positive solutions is now proved for nonlinearities f of exponential type. In order that the main theorem of the authors' paper can be applied, the only difficulty is verification of the hypothesis (F/f)′≥0. This is very delicate. Also, under the stronger regularity condition on the elliptic part, ground states with connected support are shown to be radially symmetric in the plane, and hence unique up to translations by the main theorem of Pucci and Serrin. Related results were obtained recently by Adimurthi [Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), no. 5, 895-906].
Uniqueness of ground states for quasilinear elliptic equations in the exponential case
PUCCI, Patrizia;
1998
Abstract
The boundary value problem and notation are as in previous paper of Pucci and Serrin [Indiana Univ. Math. J. 47 (1998), no. 2, 501-528]. A uniqueness theorem for positive solutions is now proved for nonlinearities f of exponential type. In order that the main theorem of the authors' paper can be applied, the only difficulty is verification of the hypothesis (F/f)′≥0. This is very delicate. Also, under the stronger regularity condition on the elliptic part, ground states with connected support are shown to be radially symmetric in the plane, and hence unique up to translations by the main theorem of Pucci and Serrin. Related results were obtained recently by Adimurthi [Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), no. 5, 895-906].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
