JQuery not working with Vuejs

You should use Vue.nextTick when using a jQuery plugin that needs the DOM to be ready.

From the vue.js documentation:

Defer the callback to be executed after the next DOM update cycle. Use it immediately after you’ve changed some data to wait for the DOM update.

In your case you should use the following implementation of the ready() method:

ready: function() {
    this.listUsers();
    Vue.nextTick(function () {
        this.installOWLcarousel();
    }.bind(this))
 }

EDIT: For Vue 2 use mounted() or created()

Add ref prop to #user element like this

<div id="user" class="owl-carousel" ref="carousel_or_anything">

Then in add mounted method to Vue component:

...
mounted: function(){
  jQuery(this.$refs.carousel_or_anything).owlCarousel();
}
...

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