We prove the Morse relations for all geodesics connecting two non-conjugate points on a class of globally hyperbolic Lorentzian manifolds. We overcome the difficulties coming from the fact that the Morse index of every geodesic is infinite, and from the lack of the Palais-Smale condition, by using the Morse complex approach. Introduction Let M be a smooth connected manifold without boundary of ...

In this paper, the boundedness and compactness of embedding from Besov Type spaces Bp(?) into tent Tq,s(?) are investigated (1 ? p q < 0 ?,s 1). As an application, Volterra integral operator T1 I1 to F(q,q-2+q/p(1-?),s) also studied.

We investigate for a bounded semigroup of linear operators S on Banach space E and vector x∈E, when relative compactness S(I−T)x every T∈S implies the orbit Sx. In particular, we derive characterizations separable spaces not containing c0 reflexivity with Schauder basis in terms such results.

The concept of intuitionistic fuzzy β-almost compactness and intuitionistic fuzzy β-nearly compactness in intuitionistic fuzzy topological spaces is introduced and studied. Besides giving characterizations of these spaces, we study some of their properties. Also, we investigate the behavior of intuitionistic fuzzy β-compactness, intuitionistic fuzzy β-almost compactness, and intuitionistic fuzz...

A variant of compactness designated as statistical has been introduced. Statistically compact subsets n-dimensional Euclidean space Rn have characterized by using Cantor-Bendixson derivative and it is further extended to the product RN.

The Palais-Smale Condition C holds for the Yang-Mills functional on principal bundles over compact manifolds of dimension ≤ 3. This was established by S. Sedlacek [17] and C. Taubes [18] Proposition 4.5 using the compactness theorem of K. Uhlenbeck [20]; see also [23]. It is well known that Condition C fails for Yang-Mills over compact manifolds of dimension ≥ 4. The example of SO(3)-invariant ...