A theorem of the ``mountain impasse'' type and semilinear elliptic problems on manifolds (Q1336345)

The aim of this paper is to consider a theorem of the mountain impasse type with no Palais-Smale condition assumed. The situation here is that of critical point at infinity when mountain pass geometry is expected to provide no critical points. The abstract framework is applied to a semilinear elliptic problem with a Laplace-Beltrami operator on a compact Riemannian manifold \(-\lambda \Delta_ M u = f(u)\) with \(f\) of subcritical growth and superlinearity at infinity.