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International Journal of Differential Equations
Volume 2010 (2010), Article ID 432759, 11 pages
http://dx.doi.org/10.1155/2010/432759
Research Article

On the Existence of Nodal Solutions for a Nonlinear Elliptic Problem on Symmetric Riemannian Manifolds

1Dipartimento di Matematica Applicata “U.Dini”, Università di Pisa, via F. Buonarroti 1/c, 56100 Pisa, Italy
2Dipartimento di Metodi e Modelli Matematici, Università di Roma “La Sapienza”, via Antonio Scarpa 16, 00161 Roma, Italy

Received 1 October 2009; Accepted 7 December 2009

Academic Editor: Thomas Bartsch

Copyright © 2010 Anna Maria Micheletti and Angela Pistoia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Given that ( 𝑀 , 𝑔 ) is a smooth compact and symmetric Riemannian 𝑛 -manifold, 𝑛 2 , we prove a multiplicity result for antisymmetric sign changing solutions of the problem 𝜀 2 Δ 𝑔 𝑢 + 𝑢 = | 𝑢 | 𝑝 2 𝑢 in 𝑀 . Here 𝑝 > 2 if 𝑛 = 2 and 2 < 𝑝 < 2 = 2 𝑛 / ( 𝑛 2 ) if 𝑛 3 .