We consider the boundary value problem Δu+|x|^{2α} u p =0, α>0, in the unit ball B with homogeneous Dirichlet boundary condition and p a large exponent. We find a condition which ensures the existence of a positive solution u_p concentrating outside the origin at k symmetric points as p goes to +∞. The same techniques lead also to a more general result on general domains. In particular, we find that concentration at the origin is always possible, provided α \notin IN.
Esposito, P., Pistoia, A., Wei, J. (2006). Concentrating solutions for the Hénon equation in R^2. JOURNAL D'ANALYSE MATHEMATIQUE, 100(1), 249-280 [10.1007/BF02916763].
Concentrating solutions for the Hénon equation in R^2
ESPOSITO, PIERPAOLO;
2006-01-01
Abstract
We consider the boundary value problem Δu+|x|^{2α} u p =0, α>0, in the unit ball B with homogeneous Dirichlet boundary condition and p a large exponent. We find a condition which ensures the existence of a positive solution u_p concentrating outside the origin at k symmetric points as p goes to +∞. The same techniques lead also to a more general result on general domains. In particular, we find that concentration at the origin is always possible, provided α \notin IN.File in questo prodotto:
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