My iPhone 6s stuck on Apple Logo

hello, my iPhone 6s stuck on apple logo. It can not be restored and updated. I have tried to contact local apple technicians, they said that the problem is in hardware and they are not able to fix it. I think to return it to an apple store in the US but I don't have a purchase receipt, I lost it. So, I would like to know if apple store can receive it and add some cash so that I can get a new one or higher version. The phone now is out of 90 days complimentary technical support. I bought it last year in July. Please advise.