Abstract. Differentiability properties of optimal value functions associated with perturbed optimization problems require strong assumptions. We consider such a set of assumptions which does not use compactness hypothesis but which involves a kind of coherence property. Moreover, a strict differentiability property is obtained by using techniques of Ekeland and Lebourg and a result of Preiss. S...

The Ambrosetti-Rabinowitz (AR) condition is crucial in variational methods. In this paper we consider a class of p-Laplacian equations without the AR condition. Using Mountain pass lemma and Ekeland variational principle, we obtain the existence and multiplicity of the solutions. These results complement some known results.

The asymptotical limit of the trajectory deened by the continuous steepest descent method for a proper closed convex function f on a Hilbert space is characterized in the set of minimizers of f via an asymp-totical variational principle of Brezis-Ekeland type. The implicit discrete analogue (prox method) is also considered.

We introduce the new concepts of e-distance, e-type mapping with respect to some e-distance and S-complete quasimetric space, and prove minimization theorems, fixed point theorems, and variational principles on an S-complete quasimetric space. We also give some examples of quasimetrics, e-distances, and e-type mapping with respect to some e-distance. Our results extend, improve, and unify many ...

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)...

We extend the classical Neyman-Pearson theory for testing composite hypotheses versus composite alternatives, using a convex duality approach as in Witting (1985). Results of Aubin & Ekeland (1984) from non-smooth convex analysis are employed, along with a theorem of Komlós (1967), in order to establish the existence of a max-min optimal test in considerable generality, and to investigate its p...

We introduce the notion of λ-spaces which is much weaker than cone metric spaces defined by Huang and X. Zhang 2007 . We establish some critical point theorems in the setting of λ-spaces and, in particular, in the setting of complete cone metric spaces. Our results generalize the critical point theorem proposed by Dancs et al. 1983 and the results given by Khanh and Quy 2010 to λ-spaces and con...