Yes, Japan's fleet of fighter aircraft are stressed responding to Chinese aerial challenges to Japan's sovereignty over distant islands:
A long-standing rivalry between China and Japan has intensified in recent years, owing in part to growing parity between the two Asian great powers. Although the competition involves many issues and spans political, economic, and security domains, the dispute over the Senkaku Islands remains a focal point. The authors examine how China has stepped up its surface and air activities near Japan, in particular near the Senkaku Islands. They survey the patterns in Chinese vessel and air activity and consider Japan's responses to date. The authors conclude that resource constraints and limited inventories of fighter aircraft pose formidable obstacles to the Japanese Air Self-Defense Force's ability to match Chinese air activity. Given China's quantitative advantage in fighter aircraft, Japan's current approach may not be sustainable.
The authors have a number of suggestions, including using ground-based air defenses to fill in for aircraft when possible.
I've suggested sending in the "robots" to defend the Senkakus:
Surface, sub-surface, aerial, and ground based robots (or remotely crewed devices, in the case of anything that can shoot) could be deployed around the Senkaku Islands. These robots would be defenders of Japanese control that will always be there, never tiring. And they could soak up every electronic and sound emission that the Chinese vessels release, for future reference.
Deploying coast guard or even navy vessels could be reserved for the most important messages.
Otherwise, let the Chinese play with the Roombas with attitude--they could transmit a message welcoming visitors to Japan and wishing them, "Have a nice visit!"
If the Japanese want to play a little rougher, like red-light camera systems, they could photograph intruding ships and planes and then send them a bill to the pilot or captain (sent to the unit) for the fee to visit Japan.
Armed robots for the really tough cases would be an option, too. With the Japanese Self Defense Forces in the background and the American armed forces on call, too.
If you combine those assets with the ability of even a single F-35 to fire the ground-based missiles at a large force of aircraft, it will be the Chinese pilots who are stressed by their challenges and not the Japanese defenders.
