Seeing as though the only helpful answers have been referencing third party libraries - here's your native javascript solution. For anyone that only wants a few lines of code rather than a stack:
The function:
Array.prototype.findValue = function(name, value){
   var array = map(this, function(v,i){
        var haystack = v[name];
        var needle = new RegExp(value);
        // check for string in haystack
        // return the matched item if true, or null otherwise
      return needle.test(haystack) ? v : null;
   });
  return array;
}
A native .map() function:
map = function(array, mapFunction) {
      var newArray = new Array(array.length);
      for(var i = 0; i < array.length; i++) {
        newArray[i] = mapFunction(array[i]);
      }
      return newArray;
}
Your object: 
(skimmed from your posted abject):
myObject = {
        name : "soccer",
        elems : [
            {name : "FC Barcelona"},
            {name : "Liverpool FC"}
        ]
    },
    {
        name : "basketball",
        elems : [
            {name : "Dallas Mavericks"}
        ]
    }
For usage:
(This will search your myObject.elems array for a 'name' matching 'FC')
var matched = myObject.elems.findValue('name', 'FC');
console.log(matched);
The result - check your console:
[Object, Object, findValue: function]
0: Object
name: "FC Barcelona"
__proto__: Object
1: Object
name: "Liverpool FC"
__proto__: Object
length: 2
__proto__: Array[0]