We prove a strong variant of the Borwein-Preiss variational principle, and show that on Asplund spaces, Stegall's variational principle follows from it via a generalized Smulyan test. Applications are discussed.

Keywords:

variational principle, strong minimizer, generalized Smulyan test, Asplund space, dimple point, porosity variational principle, strong minimizer, generalized Smulyan test, Asplund space, dimple point, porosity

MSC Classifications:

49J52 show english descriptions Nonsmooth analysis [See also 46G05, 58C50, 90C56] 49J52 - Nonsmooth analysis [See also 46G05, 58C50, 90C56]

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