I don't know whether the English text is changed after daniellevz' comment, but the current "Are these solutions applicable" sounds good & quite common to me and translates well to damoller's Portuguese version. From my point of view, the PT 'têm aplicasão' is the strangest-sounding part (as opposed to 'são aplicaveis')
But wouldn't that be used if you were talking about a specific area. Like when you were talking about a certain problem, and then say "Do these solutions apply?" rather than "do these solutions have an application?" which would be more general, like "Is there any application for these solutions?". I am not a native speaker, so I would like to know if my intuition is right.
You are adding the article "an" to the sentence (i.e. 'Do these solutions have AN application'), which isn't there in Duo's version, this giving the English sentence a different meaning, I think. The original text means 'Are these solutions applicable' (context being to a certain problem, as I understand it), or 'Do these solutions apply'. :-)
DL doesn't give context, unfortunately. On the other hand, it quite often is reasonably liberal in allowing translations. I agree with JohnGrunewald that "Do these solutions apply" is a translation that should be accepted (so I reported it in the hope that this will be done).
I am neither a native English speaker nor a native Portuguese speaker, so I am not sure if what I will say is 100% correct.
I think "Do these solutions apply?" would generally be used in a particular situation, and mean "are they applicable in this situation".
And "Are these solutions applicable?" can mean the same, or can be used in general ("is there an application for these solutions?")
"Do these solutions have an application?" would also have the more general meaning. (BTW, this answer is accepted by DL.)
So my question is, does the Portuguese also have this more general meaning, or can it also mean "Are these solutions applicable in this particular situation?"