The present paper is concerned with an elliptic problem in ℝN 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 [N-3/2] + (-1)N sequences of arbitrary small, non-radial, sign-changing solutions such that elements in different sequences are distinguished by their symmetry properties.
- Oscillatory nonlinearity
- Symmetrically distinct soltuions
ASJC Scopus subject areas
- Applied Mathematics