Geodesic
A nonlinear elliptic equation with singular potential and applications to nonlinear field equations
Journal of the European Mathematical Society, Tome 9 (2007) no. 3, pp. 355-381

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/83
Classification : 35-XX, 00-XX
Keywords: Semilinear elliptic equation, singular potential, asymptotic behavior, solitary wave 
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     author = {Marino Badiale and Vieri Benci and Sergio Rolando},
     title = {A nonlinear elliptic equation with singular potential and applications to nonlinear field equations},
     journal = {Journal of the European Mathematical Society},
     pages = {355--381},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2007},
     doi = {10.4171/jems/83},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/83/}
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Marino Badiale; Vieri Benci; Sergio Rolando. A nonlinear elliptic equation with singular potential and applications to nonlinear field equations. Journal of the European Mathematical Society, Tome 9 (2007) no. 3, pp. 355-381. doi: 10.4171/jems/83

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