(Potentially) Low GPA with No Reserach Experience, Am I Screwed for math PhD program? I am a Japanese junior student who is thinking of applying to the PhD program(Applied Mathematics/Statistics) in the U.S. for the 2021 cycle, but I think I have an incredibly low chance to be accepted to any programs.

Firstly, my GPA is really bad compared to other applicants. I have seen GPA of applicants on https://mathematicsgre.com/ and most of the people in that forum have at least a GPA of 3.8 or even 4.0. However, my overall GPA until the first semester of junior year was 3.48/4.0(Math GPA 3.5), which is really low for grad school. This was because I took too many courses and could not handle some of them(did not fail any but low grades). Moreover, my GPA in the third quarter this year is not going to be good because my grade in a literature class(it was mandatory to take it) is going to be C in S(4)-A(3)-B(2)-C(1) grading and I messed up in quantum mechanics exam. Grades in math classes are not going to be all S too. I am trying to get nice grades in this fourth quarter, but it will not be as good as average applicants.

Secondly, I literally have no research experience. From what I have seen, college students in the U.S. have an opportunity to do REUs. However, it is not the case in Japan. Math majors are not even expected to write a senior thesis and research opportunities are very limited here. I have asked my advisor about this but could not get any good results.

I still have not taken GRE, but from what I have heard, the GRE score does not matter as long as it is not astronomically bad, which does not help in my case.

Should I just give up or is there anything I can do?
I can't speak for math specifically but here is a general answer

First, don't worry about no research experience. some US undergraduates have research experience but not all. I had literally zero and I was admitted to very prestigious universities

As to GPA, there's nothing you can do about the past grades so just do the best you can on remaining classes. You can mention something about it in your cover letter if you want (ie some explanation like in your question). 3.5 is not the worst GPA in the world. 

GRE scores matter more or less at different places. Just study the best you can.

You can also make sure your research statement is well written. Find universities where there are professors whose interests match yours very well

In short I don't think you're in a hopeless situation.