We study radial solutions u = (u(1), u(2)) in an exterior domain of R-N (N >= 3) of the elliptic system -Delta u + V'(u) = 0, where V is a positive and singular potential. We look for solutions which satisfy Dirichlet boundary conditions and vanish at infinity. We prove existence of infinitely many radial solutions, which can be topologically classified by their winding numbers around the singularity of V. Furthermore, we study some qualitative properties of such solutions.
Multiple radial solutions for a class of elliptic systems with singular nonlinearities / Cingolani, S.; Lazzo, M.; Padial, J. F.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 175:1(1998), pp. 365-373. [10.1007/BF01783693]
Multiple radial solutions for a class of elliptic systems with singular nonlinearities
S. Cingolani;
1998-01-01
Abstract
We study radial solutions u = (u(1), u(2)) in an exterior domain of R-N (N >= 3) of the elliptic system -Delta u + V'(u) = 0, where V is a positive and singular potential. We look for solutions which satisfy Dirichlet boundary conditions and vanish at infinity. We prove existence of infinitely many radial solutions, which can be topologically classified by their winding numbers around the singularity of V. Furthermore, we study some qualitative properties of such solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
