可以使用哈希表（HashMap）来解决这个问题。遍历数组并使用哈希表来计数每个数字在数组中出现的次数。然后，遍历哈希表，将出现次数大于或等于n的数字添加到列表中并返回。

下面是实现该方法的Java代码示例：

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class Main {
    public static void main(String[] args) {
        int[] arr = {1, 2, 2, 3, 3, 3, 4, 4, 4, 4};
        int n = 3;
        List result = getNumbersWithNOrMoreOccurrences(arr, n);
        System.out.println(result);
        // Output: [3, 4]
    }

    public static List getNumbersWithNOrMoreOccurrences(int[] arr, int n) {
        Map frequencyMap = new HashMap<>();

        // count frequency of each number
        for (int i = 0; i < arr.length; i++) {
            if (frequencyMap.containsKey(arr[i])) {
                frequencyMap.put(arr[i], frequencyMap.get(arr[i]) + 1);
            } else {
                frequencyMap.put(arr[i], 1);
            }
        }

        // add numbers with frequency >= n to list
        List result = new ArrayList<>();
        for (Map.Entry entry : frequencyMap.entrySet()) {
            if (entry.getValue() >= n) {
                result.add(entry.getKey());
            }
        }

        return result;
    }
}