A nonlinear elliptic equation with singular potential and applications to nonlinear field equations
Marino Badiale
Università degli Studi di Torino, ItalyVieri Benci
Università di Pisa, ItalySergio Rolando
Università degli Studi di Torino, Italy
Abstract
We study existence and asymptotic properties of solutions to a semilinear elliptic equation in the whole space. The equation has a cylindrical symmetry and we find cylindrical solutions. The main features of the problem are that the potential has a large set of singularities (i.e. a subspace), and that the nonlinearity has a double power-like behaviour, subcritical at infinity and supercritical near the origin. We also show that our results imply the existence of solitary waves with nonvanishing angular momentum for nonlinear evolution equations of Schrodinger and Klein-Gordon type.
Cite this article
Marino Badiale, Vieri Benci, Sergio Rolando, A nonlinear elliptic equation with singular potential and applications to nonlinear field equations. J. Eur. Math. Soc. 9 (2007), no. 3, pp. 355–381
DOI 10.4171/JEMS/83