public class Test {

    public static void main(String[] args) throws ParseException {

        DateFormat df = new SimpleDateFormat("yyyy-MM-dd");

        Date d1Start = df.parse("2010-01-01");
        Date d1End = df.parse("2011-01-01");
        Date d2Start = df.parse("2010-06-01");
        Date d2End = df.parse("2011-06-01");
        
        System.out.println(calcOverlapDays(d1Start, d1End, d2Start, d2End));
    }

    public static int calcOverlapDays(Date range1Start, Date range1End,
            Date range2Start, Date range2End) {

        long range1StartTime = range1Start.getTime();
        long range1EndTime = range1End.getTime();

        long range2StartTime = range2Start.getTime();
        long range2EndTime = range2End.getTime();

        assert range1StartTime > range1EndTime;
        assert range2StartTime > range2EndTime;

        long overlapTime = Math.min(range1EndTime, range2EndTime)
                - Math.max(range1StartTime, range2StartTime);

        return (overlapTime < 0) ? 0
                : (int) (overlapTime / 24 / 60 / 60 / 1000 + 1);
    }
}

------解决方案--------------------
 不知道能不能满足你的要求！
Java code


        //String time1_star = "2011-01-01";
        String time1_end = "2011-05-01";
        
        String time2_star = "2011-04-01";
        //String time2_end="2011-06-01";
        SimpleDateFormat sdf = new SimpleDateFormat("yyyy-MM-dd");
        try {
            Date time1 =sdf.parse(time1_end);
            Date time2 =sdf.parse(time2_star);
            long diffDay= (time1.getTime()-time2.getTime())/(3600*1000*24);
            if(diffDay > 0){
                System.out.println("重合天数为："+diffDay);
            }else{
                System.out.println("没有重合天数");
            }
            System.out.println(diffDay);
        } catch (ParseException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }