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We consider a family of variational problems on a Hilbert manifoldparameterized by an open subset of a Banach manifold, and we discuss thegenericity of the nondegeneracy condition for the critical points. Based on anidea of B. White, we prove an abstract genericity result that employs theinfinite dimensional Sard--Smale theorem. Applications are given by proving thegenericity of metrics without degenerate geodesics between fixed endpoints ingeneral (non compact) semi-Riemannian manifolds, in orthogonally splitsemi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. Wediscuss the genericity property also in stationary Lorentzian manifolds.

Genericity of nondegenerate critical points and Morse geodesic functionals