Switch to mathematics I am studying physics and mathematics double major at undergraduate level. Recently, I found out I don't have enough eager to pursue my graduate studies in physics which is my main major. I want to comprehend and obtain a realistic sight on my chance for accepting in "good" graduate mathematics department although my main major is physics. I have had several accomplishments in physics competitions but no math honor.

Thank you very much.
You don't need to have earned any honors or prizes in math.  You do need to show that you are a strong student in general, and that you have sufficient background in math to be able to hit the ground running.

Physics and math are very close and give you a great deal of fluidity, especially in the direction you want to go -- as long as you have taken enough math classes.  (Some people graduate in physics with the bare minimum of math classes -- with PDEs as the most advanced class taken -- and they would have trouble making this switch -- but you are not one of those people.)