Exegesis:
hoi de epi tēs petras (scil. eisin) hoi hotan akousōsin meta charas dechontai ton logon ‘the (people) on the rock (are) those who, when they hear (the word) receive it with joy.’ For hoi epi tēs petras cf. on v. 12. dechomai here of receiving and acknowledging the word of God.
kai houtoi rizan ouk echousin ‘and those have no root,’ as if the subject were the seed that fell on the rock, and not the people which can be compared with the seed that fell on the rock. kai is here ‘and yet,’ or ‘but.’ riza, cf. on 3.9. houtoi refers back to hoi epi tēs petras.
hoi pros kairon pisteuousin ‘who believe for a while.’ This relative clause takes up meta charas dechontai, and, at the same time, applies the statement that they have no root: they believe for a while only.
kairos here ‘(short) period of time.’ pros kairon ‘for a short period,’ ‘for a while.’
en kairō peirasmou aphistantai ‘in a time of trial they fall away.’ kairos has a somewhat wider scope here than in pros kairon. For peirasmos cf. on 4.13, but here the meaning is passive, and implies that the faith of the believers is put to the test.
aphistamai ‘to become apostate,’ ‘to fall away’ (cf. 1 Tim. 4.1; Heb. 3.12).
Translation:
Receive it with joy. The verb complies mental consent, acceptance, approval. With joy, or, ‘joyfully,’ ‘and rejoice,’ ‘while (or, and) their heart was glad,’ etc.
These have no root, or, ‘do not root well’ (cf. Tboli); or, again making explicit the underlying simile, ‘these are as though not (really) taking root,’ ‘these are like seed that does not strike (much) root.’
In time of temptation, or, changing to the verbal clause, ‘when they are tempted, or, put to the test’ (cf. Balinese, Tae’), or, where an active construction is preferable, ‘when the devil tests them, or, tries to make them fall away.’ For ‘to tempt’ see also on 4.2a. Renderings like ‘hardship/trouble’ are not advisable.
Fall away, or, ‘draw back,’ ‘go astray’ (Marathi), ‘turn away/aside’ (Batak Toba, Sranan Tongo), ‘desert,’ lit. ‘fly back’ (as a spring does) (Toraja-Sa’dan), ‘become-renegades’ (Javanese).
Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.