Many people with knee problems have difficulty on stairs. They may require a handrail to get up or down stairs or need to take them one at a time. It may be because of pain or instability but also can be because of weakness or balance problems which have nothing to do with the knee.
Walking up and down stairs places huge loads on the patellofemoral joint. If there is arthritis in the joint then loading it creates pain at the front of the knee. This causes the quadriceps muscle to release which can give the sensation of the knee giving way or that the leg is not strong enough to take the weight of the body. This is not true giving way or instability of the knee which is the result of a ligament injury.
Other causes of knee pain can also make life difficult on stairs such as meniscal tears or loose bodies. If there is a ligament injury to the knee it is typically made worse with single leg loading of the knee. If the PCL (posterior cruciate ligament) is torn then walking down stairs allows the femur to slide forward on the tibia which loads the patella and can create anterior knee pain. There may not be the sensation of instability but you may find that a handrail makes it easier to walk on the knee and reduces anterior knee pain.