Edit in JSFiddle

var Core = {
    screenwidth: "1024px",
    init: function () {
        this.render();
    },
    render: function () {
        $('#container').css("width", this.screenwidth).html("Default Render Function");
    },
    utli: function () {
        $('#container').append("<p>Core utility function Called</p>");
    },
};

var mobileLib = {
    init: function () {
        this.screenwidth = "320px";
        this.render();
        this.utli();
    },
    render: function () {
        $('#container').css("width", this.screenwidth).html("Mobile Render");
    }
};

$(document).ready(function () {
    mobileJS = $.extend(true, Core, mobileLib);
    mobileJS.init();
});
<div id="container"></div>