In general, Shakespeare's Romeo and Juliet points more toward the fact that such impetuous, passionate love as Romeo and Juliet share is not genuine love and is likely to bring instability and heartache, as we see in Friar Laurence's warning to Romeo just prior to conducting the wedding ceremony: "These violent delights have violent ends" (II.vi.9). However, if one looks at things out of context, one might be able to interpret a few passages as showing that Romeo and Juliet may eventually be capable of developing a mature love.
One example of such a passage is Juliet's response to Romeo in Friar Laurence's cell just before the wedding ceremony. When Juliet first enters the room, Romeo asks her to say so if her joy is still as rich as his due to the prospect of their marriage and asks if she still sees it as right. Juliet's response essentially communicates that her joy is far greater than words can express. She ends with the the lines, "But my true love is grown to such excess / I cannot sum up sum of half my wealth," meaning her love has grown so much since she last saw him that she can't express even half her love in words (II.iv.33-34). Since love grows as it matures, we can say the professed growth of her love is a sign that she can love maturely.
However, it's important to see the lines in context with the greater scene. Romeo has just said the following passionate lines:
... then sweeten with thy breath
This neighbour air, and let rich music's tongue
Unfold the imagin'd happiness that both
Receive in either by this dear encounter. (26-29)
On the one hand, we can interpret references to "thy breath" and "tongue" as references to speaking words since words are spoken through breath and the movement of tongues. However, on the other hand, many have also interpreted these lines as referring to kissing and have actually depicted the couple endlessly kissing during this exchange, leading Friar Laurence to end the scene by saying he'll get them married very quickly and not leave them alone until they are indeed married. Therefore, if we take into account the degree of passion in this scene, we are left to reflect as Friar Laurence did that such impetuous, passionate love is not genuine and likely to die as speedily as it begins, which is the exact opposite of a mature love.
Another passage we may be able to loosely interpret as showing that Romeo and Juliet are capable of a mature love can be seen the moment Juliet learns from Nurse that Romeo has just been sentenced to banishment for slaying Tybalt. When Nurse asks Juliet, "Will you speak well of him that kill'd your cousin?," Juliet's response is to rhetorically ask, "Shall I speak ill of him that is my husband?," which is to say that she is devoted to still honoring him despite this misdeed (III.ii.101-102). Juliet's firm devotion to thinking honorably of her husband despite Tybalt's murder can be taken as a sign that she is capable of mature love since it shows she is capable of strong devotion.
Yet, again, interpreting just this line is taking things out of context considering that, in a previous passage, Juliet just devoted 12 lines to questioning Romeo's goodness and honesty and even going so far as to call him a "villain." So, can we really interpret Juliet as being capable of any maturity at all? Or is she simply the impetuous sort who lets her emotions change with the changing winds?