This is shown clearly through his prayer at the beginning of the letter. I’ll provide the text below form the NAS95.

“Paul and Timothy, bondservants of Christ Jesus, To all the saints in Christ Jesus who are in Philippi, including the overseers and deacons: (2) Grace to you and peace from God our Father and the Lord Jesus Christ.
(3) I thank my God in all my remembrance of you, (4) always offering prayer with joy in my every prayer for you all, (5) in view of your participation in the gospel from the first day until now. (6) For I am confident of this very thing, that He who began a good work in you will perfect it until the day of Christ Jesus. (7) For it is only right for me to feel this way about you all, because I have you in my heart, since both in my imprisonment and in the defense and confirmation of the gospel , you all are partakers of grace with me. (8) For God is my witness, how I long for you all with the affection of Christ Jesus. (9) And this I pray, that your love may abound still more and more in real knowledge and all discernment, (10) so that you may approve the things that are excellent, in order to be sincere and blameless until the day of Christ; (11) having been villed with teh fruit of righteousness which comes through Jesus Christ, to the glory and praise of God.”

True, it’s not a prayer proper, rather Paul describing his prayer. But notice how even in his prayer he describes his affection for them as “the affection of Jesus Christ.” In fact, his desire is that they would be filled with the fruit of righteousness that comes through Jesus Christ.

As for application, it is this, for me. To consider my relationship to others in view of the affection of Jesus Christ. To consider not just that Jesus loved the world, but to consider how he loved it. His love, both selfless and powerful was expended for the sake of the beloved, not for his own sake. And yet, through it, God glorifies him so that he is not empty, but filled with the love of the Father.

In turn, we can so love the world should we choose. It is a hard grueling love, sometimes. Difficult, challenging, inexplicable, and incredible…sometimes downright nonsensical to our human minds. And yet, though we should expend ourselves for the sake of the beloved other, we are not empty, for God, our Father, fills us with his love.

Perhaps as we pray, we could learn something from Paul. We learn to pray for others, and to consider them through the eyes of Jesus. It might not be a bad idea to even borrow Paul’s phrase “with the affection of Jesus Christ.”