The main theorem establishes uniqueness of positive solutions u=u(r) of quasilinear problems satisfying genearl natural conditions on the elliptic part and on the nonlinear terms. A principal component of the proof is a new (generalized) Erbe-Tang identity for nonnegative solutions [L. H. Erbe and M. X. Tang, J. Differential Equations 138 (1997), 351-379]. The theorem is applicable to the radial m-Laplacian, m>1, as well as to the general prototype interesting in applications. Also Neumann-type problems in exterior domains are studied. The results extend or complement uniqueness theorems of M. K. Kwong [Arch. Rational Mech. Anal. 105 (1989), 243-266], C. C. Chen and C. S. Lin [Comm. Partial Differential Equations 16 (1991), 1549-1572], E. Yanagida [Arch. Rational Mech. Anal. 115 (1991), 257-274], G. Citti [Boll. Un. Mat. Ital. B 7 (1993), 283-310], B. Franchi, E. Lanconelli and Serrin [Adv. Math. 118 (1996), 177-243], C. Cortázar, M. Elgueta and P. L. Felmer [Arch. Rational Mech. Anal. 142 (1998), 127-141], and others cited therein.
Uniqueness of ground states for quasilinear elliptic operators
PUCCI, Patrizia;
1998
Abstract
The main theorem establishes uniqueness of positive solutions u=u(r) of quasilinear problems satisfying genearl natural conditions on the elliptic part and on the nonlinear terms. A principal component of the proof is a new (generalized) Erbe-Tang identity for nonnegative solutions [L. H. Erbe and M. X. Tang, J. Differential Equations 138 (1997), 351-379]. The theorem is applicable to the radial m-Laplacian, m>1, as well as to the general prototype interesting in applications. Also Neumann-type problems in exterior domains are studied. The results extend or complement uniqueness theorems of M. K. Kwong [Arch. Rational Mech. Anal. 105 (1989), 243-266], C. C. Chen and C. S. Lin [Comm. Partial Differential Equations 16 (1991), 1549-1572], E. Yanagida [Arch. Rational Mech. Anal. 115 (1991), 257-274], G. Citti [Boll. Un. Mat. Ital. B 7 (1993), 283-310], B. Franchi, E. Lanconelli and Serrin [Adv. Math. 118 (1996), 177-243], C. Cortázar, M. Elgueta and P. L. Felmer [Arch. Rational Mech. Anal. 142 (1998), 127-141], and others cited therein.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
