Kristály, Alexandru; Marzantowicz, Waclaw Multiplicity of symmetrically distinct sequences of solutions for a quasilinear problem in \({\mathbb{R}}^N\). (English) Zbl 1143.35045 NoDEA, Nonlinear Differ. Equ. Appl. 15, No. 1-2, 209-226 (2008). Summary: The present paper is concerned with an elliptic problem in \({\mathbb{R}}^N\) which involves the \(p\)-Laplacian, \(p > N\), (\(N = 4\) or \(N \geq 6\)), 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. Cited in 6 Documents MSC: 35J60 Nonlinear elliptic equations 35J20 Variational methods for second-order elliptic equations 35J70 Degenerate elliptic equations 35D05 Existence of generalized solutions of PDE (MSC2000) Keywords:oscillatory nonlinearity; symmetrically distinct solutions; quasilinear elliptic problem PDFBibTeX XMLCite \textit{A. Kristály} and \textit{W. Marzantowicz}, NoDEA, Nonlinear Differ. Equ. Appl. 15, No. 1--2, 209--226 (2008; Zbl 1143.35045) Full Text: DOI