The main purpose of this paper is to establish a three critical points result without assuming the coercivity of the involved functional. To this end, a mountain-pass theorem, where the usual Palais-Smale condition is not requested, is presented. These results are then applied to prove the existence of three solutions for a two-point boundary value problem with no asymptotic conditions.

The concept of convex-compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in lieu of compactness in a variety of cases. In particular, we show that bounded-in-probability, convex and closed subsets of the space L+(Ω,F , P) of finite-va...

In an L-topological space we present good definitions for local compactness, weak local compactness and relative local compactness. We obtain the equivalence of these properties in a Hausdorff space and we also obtain a one point compactification theorem.

The Abstract Compactness Theorem of Makowsky and Shelah for model theoretic logics is shown to be an immediate consequence of a general characterization of topological spaces having [ ; ]-compact products, when applied to spaces of structures endowed with the natural topology induced by the de…nable classes of a logic L. In this context, the notion of an ultra…lter U being related to L correspo...

In this paper, we study the moduli space of frozen planet orbits in Helium atom for an interpolation between instantaneous and mean interactions show that is compact.

We establish an existence result for semilinear elliptic problems with the associated functional not satisfying the Palais-Smale condition. The nonlinearity of our problem does not satisfy the Ambrosetti-Rabinowitz condition.