my border collie is having trouble climbing stairs,he is 11

Good Morning and welcome! I am Dr. Loretta, a licensed veterinarian and I am happy to answer your question.

I am so sorry to hear about your guy.

Most likely your guy has suffered an injury to a disc in his back or has Discospondylitis which is arthritis interfering with the nerve supply. This is very common in older dogs because of their conformation. Since he does not have any digestive issues, this is the most likely cause for his pain. Since this is deep within the vertebrae, he will not show pain when you touch or palpate these areas. This can happen when he jumps up or down on something or just moves the wrong way. or climbig stairs. 

The best thing you can do for now as long as your guy is eating well now, is to give him aspirin at 5 mg per pound every 12 hrs. This will decrease the inflammation that is causing his pain and start to stabilize this disc. Do not allow him to jump on or off anything or even climb stairs to allow this disc to stabilize.

It is best to have your vet examine him to be sure that this is the case and that this treatment is appropriate.
 Because of your guys age, it is also recommended to give a daily supplement of Glucosamine/Chondroitin available at the pet store. This will add lubrication to his joints to decrease pain.

Does that make sense to you?

Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please REPLY so I can clarify for you.

Sincerely, ***** *****