οὐ is sometimes used where we expect μή.
a. Where οὐ stands in a clause introduced by εἰ or other words after which μή might be expected ( cross2698). Thus,
ὄφρα καὶ οὐκ ἐθέλων τις ἀναγκαίῃ πολεμίζοι
b. Where οὐ goes strictly with the leading verb though it stands with the infinitive. Thus, βουλοίμην δ' ἃν οὐκ εἶναι τόδε
ὀμώμοκεν οὐ χαριεῖσθαι . . . ἀλλὰ δικάσειν κατὰ τοὺς νόμους
c. Where οὐ in a contrast goes closely with a following word or words, or stands in a partial parenthesis. Thus, κελεύων οὐκ ἐν τῇ ἐκκλησίᾳ ἀλλ' ἐν τῷ θεά_τρῳ τὴν ἀνάρρησιν γίγνεσθαι (he has violated the law)
ὁμολογοίην ἂν ἔγωγε οὐ κατὰ τούτους εἶναι ῥήτωρ
ὑ_μᾶς νῦν ἀξιοῦντες οὐ ξυμμαχεῖν, ἀλλὰ ξυναδικεῖν
d. When a compound negative with the infinitive repeats οὐ used with the leading verb. Thus, (ὁ νόμος)
οὐκ ἐᾷ εἰσιέναι, οὗ ἂν ᾖ ὁ τετελευτηκώς, οὐδεμίαν γυναῖκα
e. When οὐδείς may be resolved into οὐ and τὶς, οὐ going with the leading verb. Thus, οὐδενὸς ( = οὔ τινος) ἁμαρτεῖν . . . δίκαιός ἐστιν
ἀξιῶ ἐγὼ ὧν ὀμωμόκατε παραβῆναι οὐδέν
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].