MongoDB check field existence and partial match

db.getCollection('merged_authors').find({last_name:
'Wang','first_name': {'$regex': 'Junmin'}, user_id:{$exists:true} })

router.get('/merged_author/', function (req, res, next) {
  var first_name = req.query.first_name;
  var last_name = req.query.last_name;
  var full_name = req.query.full_name;
  var middle_name = req.query.middle_name;
  var page = req.query.page;
  if (page == null) {
    page = 1;
  }
  var per_page = req.query.per_page;
  if (per_page == null) {
    per_page = 25;
  }
  var name_results = [];
  var condition = {};
  if (first_name != undefined) {
    condition_first_name ={};
    condition_first_name["$regex"] = first_name;
    condition["first_name"] = condition_first_name;
  }
  if (last_name != undefined) {
    condition["last_name"] = last_name;
  }
  if (middle_name != undefined) {
    condition["middle_name"] = middle_name;
  }

  condition["user_id"] = {$exists: true};
  console.log(condition);
  KMMergedAuthors.find(condition)
    .sort(
      buildSortClause(req)
    )
    .limit(50)
    .exec()
    .then(function (allMergedAuthors) {
      res.json(allMergedAuthors);
    });
});