On the existence of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds (Q606234)

Summary: Given that \((M,g)\) is a smooth compact and symmetric Riemannian \(n\)-manifold, \(n\geq 2\), we prove a multiplicity result for antisymmetric sign changing solutions of the problem \(-\varepsilon^2\Delta_gu+u=|u|^{p-2}u\) in \(M\). Here, \(p>2\) if \(n=2\) and \(2<p<2^*=2n/(n-2)\) if \(n\geq 3\).