Let's analyze your sentence. We can start by clarifying that "there" is not the real subject of the verb. It's just a dummy subject. Your real subject is "shortage".
We can also agree, surely, that "applications" is not the subject, though we can take the noun phrase "no shortage of applications" as the subject in full. In any event, the form of the verb "to be" is going to have to accord with "shortage".
With that out of the way, let's look at the word "shortage".
"Shortage" appears at first blush to be a singular noun. As such, it would take a singular verb, i.e. "is". But is there anything else to consider?
There is. Nouns classified as collective nouns can take a plural verb, in what's called notional agreement. This is because although they themselves are singular, notionally they refer to a collection of things, or a plurality. They can be thought of as containing a plurality, and because of that, they can take a plural verb form. For example:
- a number of things are...;
- a set of pieces are...;
- a host of angels are....
Now, it's common advice that when the members of the plurality implied by a collective noun are considered to be acting in unison, it's appropriate to use the singular form of the verb, whereas when the members of the plurality are acting as individuals, it's appropriate to use the plural. But this would seem to be a matter of perspective.
In any event, all of this about collective nouns might be what you're getting at with your preference for the plural form of the verb, "are".
Ask yourself, though, whether "shortage" really falls into the category of collective nouns. Would it contain, notionally, any members, any "applications", within itself? Arguably not, even though it is qualified by the word "applications". This is because a shortage is a lack, a deficiency, and as such, arguably not a collection of things.
If "shortage" is not a collective noun, the verb should accord with it in its explicit form, which is singular, and not with some notional plurality implied by it, such as "applications" – because in fact it does not encompass such a plurality.
Ah, but hold everything. One could also, perhaps, conceive of "shortage" as a number of missing things, and so, in that sense, a collective of things notionally off together somewhere. Consider this phrase:
- ... a shortage of five applications.
In this case, it becomes clearer that a "shortage" might contain a notional plurality. It's still questionable, perhaps, because the implication of "shortage" is that those applications don't actually exist.
If you do see "shortage" as collective, though, you can still ask yourself whether it justifies the use of a plural verb, because of the members acting separately, or whether a singular verb is appropriate, because of some "togetherness" of existence or action (or perhaps *non-*existence or *non-*action).
There is one more aspect to consider, and that is, even if you argue that "shortage" is a collective noun, you may have a further problem: the negative construction of your sentence, which itself denotes a lack. (With "no shortage", we have a lack of a lack, as it were, but that's neither here nor there.) I've already suggested above that it's hard to find a plurality of something in a lack of something. And absence has a certain unity that, as the subject of a sentence, seems to demand a singular verb.
Let's try some more sentences:
- There is a shortage of applications. Some applications exist, but a shortage also exists. The shortage is a lack of applications. Seems fine.
- There is no shortage of applications. Just the negative of the above. Some applications exist. No shortage exists. Seems okay too.
- There are a shortage of applications. Some applications exist, but a shortage also exist(s). Isn't the shortage some kind of entity that exists outside of the existing applications, though? The shortage relates to applications, but does it contain any applications? Is it a plurality, or, in its manifestation of lack, is it a unity? If a plurality, are its supposed members acting in unison, or individually on their own, in performing their absence?
- There are no shortage of applications. All required applications exist. No shortage exist(s). Is the shortage a unity, or a plurality? Does it make sense to say are the shortage a unity or a plurality? Is anything contained by the shortage? Are any applications contained by it? (Does it even, notionally, exist?!)
Some things for you to ponder.
RegDwigнt's answer gives corpus usage stats, which may suggest a direction of inquiry, but are, in the end, of little use for one's own conceptualization of the language issue under examination. For what it's worth, my own search of the same two corpora found "there is no shortage of" outnumbering "there are no shortage of" 217:8 in the US and 63:0 in Britain, so you might want to learn how to use the corpora yourself to see if the numbers are reliable. But all we get from the usage stats anyway is that some people have said the phrase one way, and some have said it another. We don't know if they put any thought into it, or if the ostensible "pluralists" simply misidentified the subject of their verb. (Which suggests that perhaps RegDwigнt's answer is oversimplified, to quote a certain brash assertion therein.)
In other words, to come to terms with the sentence at hand, some direct and explicit analysis of the particular words in question is useful.
In my view, three obstacles to the plural verb form are:
- Treating "shortage" as collective is a questionable choice, given that it can hardly be considered to contain any notional members.
- If it is collective, the unified action or existence of its notional members may justify the singular verb anyway.
- The negative construction of the sentence denotes an absence that may itself justify treatment of the subject as a unity, i.e. as singular.
On the other hand:
- The counterpoint to 1 is a shortage of five applications.
- The counterpoint to 2 is that it may be a matter of perspective in any event.
- The counterpoint to 3 is in a comment by Edwin Ashworth that I reproduce below*.
Some further points:
- "There is" is commonly used, at least colloquially, when "there are" might seem appropriate based on the real subject of the sentence, particularly in contracted form, as FumbleFingers points out*.
- And as FumbleFingers also points out*, in a complementary comment to Edwin Ashworth's about lack (both of which I may do better justice to in a further edit at a later date, but in any event are currently copied below for your analytical pleasure), either one can be part of a stock phrase referring to the noun considered most important in the sentence. In your sentence this could lead to an accord between the verb "are" and the word "applications". Arguably, though, this would just be a case of failure to identify the real the subject of the sentence.
- The above could affect the stats of any usage survey. Without looking into it, so could the fact that we don't know whether a mass noun or a plural noun comes after "there is no shortage of" in any particular item contained in the results (e.g. there is no shortage of water).
In the end, my own preference is for "there is a shortage of applications" and "there is no shortage of applications". And I think that's what I'd say when caught off guard and not given the chance to think about it.
In any event, you can probably treat a shortage as notionally plural without a second thought when you're talking about a shortage of dwarves (but perhaps not if you're saying there is no shortage of dwarves).
* In the event that I don't get around to a cleanup for a while, I've copied here the astute comments I refer to above, lest they disappear:
@RJH 'The majority of the population remain unconvinced' is an accepted coding of '42 763 785 (say) people in the country remain unconvinced'. I've found plenty of internet examples of the form 'There are no lack of restaurants in the area' coding for 'there are ample ...'. And 'shortage' and 'lack' are pretty close. Though yes, I'd use 'is' here. – Edwin Ashworth
I think you're starting off on the wrong foot with your very first paragraph. Bear in mind that (contracted) there's is commonly used to replace there are as well as there is. By summarily dismissing the significance (and thus, influence) of the dummy pronoun there you're ignoring one of the reasons why people don't always "talk proper". – FumbleFingers
@RJH: There are no shortage of examples of people having such notions. Forget the plurality of "shortage" - the sequence there is/are no shortage is pretty much a stock phrase/cliche where the important noun is the thing which there is/are plenty of. In this case, the plural countable noun applications. Obviously not everyone thinks that way (and those that do probably don't do it on every possible occasion). But it occurs reasonably often, and it certainly doesn't grate on my ears. – FumbleFingers