(ps)-weak Lower Semicontinuity in One-dimension: a Necessary and Sufficient Condition
نویسندگان
چکیده
The (PS)-weak lower semicontinuity property has been introduced in Vasiliu and Yan [10] for general continuously differentiable functionals on Sobolev spaces in connection with the Ekeland variational principle and the direct method of calculus of variations. In this paper, we give a necessary and sufficient condition of this property for the functionals in one-dimension of the simple type I(u) = R 1 0 f(u̇(t)) dt on the space W ((0, 1);R).
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