Or even heavily functional styles in non functional/non memory managed languages. What sort of techniques are there to deal with problems like intermediate garbage? Cleaning up after lazynizess/thunk allocated memory. Performance(since you can't easily share resources between immutable variables if you have to track its progress to deallocate it(smart pointers?)
You might be interested in programming languages with linear or uniqueness types, these can manage resources (and memory in particular). Recent examples: ATS and LinearML.
There have been attempts at "region-based memory management" (e.g. Cyclone), but they haven't lifted off just yet -- regions also allow for (earlier) memory reclamation, but they aren't enough (e.g., there are programs which, when run with region-based memory management, will exhibit unacceptable performance). The two schemes could be mixed, I think.
Back to your question, some ATS programs can run without garbage collection. (I won't say that such programs are written in "functional" style, such as in SML, but in a mix of imperative and first-order functional style.)