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 −ε2Δgu + u = |u|p−2u in M. Here p > 2 if n = 2 and 2 < p < 2∗ = 2n/(n − 2) if n ≥ 3.
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