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Proceedings of the London Mathematical Society Advance Access originally published online on January 10, 2007
Proceedings of the London Mathematical Society 2007 94(2):497-519; doi:10.1112/plms/pdl020
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© 2007 London Mathematical Society

On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity

Pierpaolo Esposito1, Monica Musso2,3 and Angela Pistoia4

1 Dipartimento di Matematica
Università degli Studi ‘Roma Tre’
Largo S. Leonardo Murialdo 1–00146 Rome Italy
esposito{at}mat.uniroma3.it
2 Departamento de Matemática
Pontificia Universidad Catolica de Chile
Avenida Vicuña Mackenna 4860 Macul Santiago Chile
3 Dipartimento di Matematica
Politecnico di Torino Corso Duca degli Abruzzi
24–10129 Turin Italy
monica.musso{at}polito.it
4 Dipartimento di Metodi e Modelli Matematici
Università di Roma ‘La Sapienza’
00100 Rome Italy
pistoia{at}dmmm.uniroma1.it

Received 28 October 2005. Revision received 14 June 2006.

We study the existence of nodal solutions to the boundary value problem – {Delta} u = |u|p – 1u in a bounded, smooth domain {Omega} in R2, with homogeneous Dirichlet boundary condition, when p is a large exponent. We prove that, for p large enough, there exist at least two pairs of solutions which change sign exactly once and whose nodal lines intersect the boundary of {Omega}.


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