Sentence examples for compact conditions from inspiring English sources

Subsequently, Benchohra and Ntouyas [10] discussed second order differential equation under compact conditions.

Ntouyas and Tsamatos [14] studied the nonlocal semilinear differential equations with compact conditions.

Remark 3.1 In Theorem 3.1, f is a discontinuous map and has no compact conditions.

Secondly, compared with [15], the relative compact conditions we used are weaker.

Benchohra and Ntouyas [13] discussed second-order differential equations under compact conditions.

In this paper, we extend and prove Ky Fan's Theorem for discontinuous increasing maps f in a Banach lattice X when f has no compact conditions.

If is compact, condition (i) is satisfied trivially.

Cerami [23] presented a weaker compact condition than the above classical ( PS ) c condition.

That is, the proof of our compact condition is more simple than that in [8].

In this paper, assuming a natural sequentially compact condition we establish new fixed point theorems for Urysohn type maps between Fréchet spaces.

To obtain a homoclinic solution of (5), some compact condition is needed, so weighted sequence spaces (l_{eta}^{p}) are also introduced in this section.