Sentence examples for which is bounded for from inspiring English sources

which is bounded for fixed.

Here, we construct some super-solution to the problem, which is bounded for any (T>0).

It turns out that the existence of such a sequence is actually equivalent to the existence of a function which is bounded from below and such that for each, (3.3).

which is bounded in V for any fixed ε ∈ ( 0, 1 ).

According to Theorem 4.1, system (5.1) has a unique uniformly asymptotically stable almost periodic solution which is bounded by Ω for all n ∈ Z +. □.

A metric space is said to have normal (resp., uniform normal) structure if there exists a convexity structure on such that (resp., for some constant for all which is bounded and consists of more than one point. In this case is said to be normal (resp., uniformly normal) in.

We say that satisfies the Palais-Smale condition if any sequence for which is bounded and as possesses a convergent sequence.

If any sequence for which is bounded and as possesses a convergent subsequence in, we say that satisfies the Palais-Smale condition.

We say that satisfies the Palais-Smale condition if any sequence for which is bounded and as possesses a convergent subsequence in.

We say that satisfies the Palais-Smale condition (PS) if every sequence for which is bounded in and (as possesses a convergent subsequence. To prove the existence of a critical point of the functional we use the Saddle Point Theorem which is proved in Rabinowitz [9] (see also [10]).

Let be a real Banach space,, that is, is a continuously Fréchet differentiable functional defined on, and is said to satisfy the Palais-Smale condition (P-S condition), if any sequence for which is bounded and as possesses a convergent subsequence in.