ὅσοι δὲ ἔλαβον αὐτόν ἔδωκεν αὐτοῖς ἐξουσίαν τέκνα θεοῦ γενέσθαι τοῖς πιστεύουσιν εἰς τὸ ὄνομα αὐτοῦ
But as many as received him, to those who believe in his name, he gave them power to become sons of God,
Thayer1 describes the sense of ἐξουσίαν (exousian) in this verse as "physical and mental power; the ability or strength with which one is endued, which he either possesses or exercises." The sense of the verse is that Jesus gave men the ability, the power, to become sons of God. Without him, this would not be possible.
ταῦτα δὲ γέγραπται ἵνα πιστεύσητε ὅτι ὁ Ἰησοῦς ἐστιν ὁ Χριστὸς ὁ υἱὸς τοῦ θεοῦ καὶ ἵνα πιστεύοντες ζωὴν ἔχητε ἐν τῷ ὀνόματι αὐτοῦ
But, these [things] are written so that you may believe that Jesus is the Christ, the son of God, and so that you may have life in his name.
If I understand your question correctly, it focuses on the word "might" or "may," which I take it, you think expresses a degree of uncertainty.
In this particular verse, we have ἵνα πιστεύσητε and ἵνα...ἔχητε. In other words, we have the conjunction ἵνα followed by a verb in the aorist tense, subjunctive mood.
This syntax is actually quite common in the New Testament. It is certainly true that these types of phrases are often translated in the KJV by the English word "might" or "may," but I would be very hesitant at asserting that the author intended the reader to understand the phrase as though expressing uncertainty (which the reader may assume when he reads the words "may" or "might").
Daniel B. Wallace writes,2
The most frequent use of ἵνα clauses is to express purpose. In classical Greek, this idea would have been expressed more often by the infinitive. The focus is on the intention of the action of the main verb, whether accomplished or not. In keeping with the genius of the subjunctive, this subordinate clause answers the question Why? rather than What? An appropriate translation would be in order that, or, where fitting, as a simple infinitive (to...).
We must not suppose tha this use of the subjunctive necessarily implies any doubt about the fulfillment of the verbal action on the part of the speaker. This may or may not be so; each case must be judged on its own merits. The subjunctive is used, however, because it answers the implicit deliberative question.
The idea, then, is that "these things are written" in order for you to believe. Had these things not been written, how could you, or why would you, have believed? Yet, herein these things are written as a testimony, a witness (cp. John 21:24), that Jesus did these things, and that he is the Christ, the son of God. People believe in him in order to have eternal life.
There is no uncertainty here. The individuals responsible for the fourth gospel confess that they wrote those things in order for people to believe in Jesus. And, by believing in Jesus, these people shall have eternal life. Both ἵνα clauses are what are known as "telic," i.e. they express a goal or purpose (Greek τέλος).
- The goal of writing these things? In order for people to believe in Jesus.
- The goal of people believing in Jesus? In order for people to have eternal life.
1 Peter 3:18
ὅτι καὶ Χριστὸς ἅπαξ περὶ ἁμαρτιῶν ἔπαθεν δίκαιος ὑπὲρ ἀδίκων ἵνα ἡμᾶς προσαγάγῃ τῷ θεῷ θανατωθεὶς μὲν σαρκὶ ζῳοποιηθεὶς δὲ τῷ πνεύματι
The meaning and translation of this verse is debated. I wouldn't construct any theological doctrines based on it alone, nor will I offer my own translation or interpretation at this time.
1 Joseph Henry Thayer: A Greek-English Lexicon of the New Testament, p. 225. American Book Company: New York, 1889. Web.
2 Daniel B. Wallace: Greek Grammar: Beyond the Basics, p. 472. Zondervan: Grand Rapids, 1996.