Abstract.
The present paper is concerned with an elliptic problem in \({\mathbb{R}}^N\) which involves the p-Laplacian, p > N, (N = 4 or N ≥ 6), while the nonlinear term has an oscillatory behaviour and is odd near an arbitrarily small neighborhood of the origin. A direct variational argument and a careful group-theoretical construction show the existence of at least \(\left[\frac{N-3}{2}\right] + (-1)^N\) sequences of arbitrary small, non-radial, sign-changing solutions such that elements in different sequences are distinguished by their symmetry properties.
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Alexandru Kristály: The research of A. Kristály was supported by the CNCSIS, project no. AT 8/70.
Waclaw Marzantowicz: The research of W. Marzantowicz was supported by KBN grant 1PO3A 03929.
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Kristály, A., Marzantowicz, W. Multiplicity of symmetrically distinct sequences of solutions for a quasilinear problem in \({\mathbb{R}}^N\) . Nonlinear differ. equ. appl. 15, 209–226 (2008). https://doi.org/10.1007/s00030-007-7015-7
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DOI: https://doi.org/10.1007/s00030-007-7015-7