Sentence examples for examples satisfying from inspiring English sources

We provide some examples satisfying such a local boundedness property, and thus have Gaussian bounds for their Green's functions.

There exist examples satisfying Theorem 1.1.

Some basic examples satisfying (F) are (1) (f(s)=as^{kappa}), where (a, kappa>0).

The results obtained include several special cases and extend previous results; two examples satisfying the assumptions are also presented.

However we will give some examples satisfying our hypotheses, where oblique boundary operators arise naturally through our domain convexity conditions.

There are some typical examples satisfying all conditions of Definition 1.3 constructed as follows: let,, where is an integer.

Now we give an example satisfying our main result.

In this section, we give an example satisfying the conditions in hypothesis (H).

A typical example satisfying these assumptions on V is (frac{1}{vert xvert ^{alpha}}) for some (alpha>0).

In Section 4, we present an interesting example satisfying our Theorem 1.1 but not satisfying the theorem in [19].

Now, we introduce an example satisfying the hypotheses of Theorem 2.3 to support the useability of our results.