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Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent |
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| Authors: | Pierpaolo Esposito Angela Pistoia |
| Institution: | a Dipartimento di Matematica, Università degli Studi “Roma Tre”, Largo S. Leonardo Murialdo, 1, 00146 Roma, Italy b Departimento de Matematica, Pontificia Universidad Catolica de Chile, Avenida Vicuna Mackenna 4860, Macul, Santiago, Chile c Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy d Dipartimento di Metodi e Modelli Matematici, Università di Roma “La Sapienza”, Via Scarpa, 16, 00166 Roma, Italy |
| Abstract: | We consider the boundary value problem Δu+up=0 in a bounded, smooth domain Ω in R2 with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Ω which ensure the existence of a positive solution up concentrating at exactly m points as p→∞. In particular, for a nonsimply connected domain such a solution exists for any given m?1. |
| Keywords: | 35J60 35B33 35J25 35J20 35B40 |
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