Hey! As mentioned by u/White___Velvet the r/AskHistorians booklist is a fantastic place to turn for resources on the topic. If you are interested on some additional recommendations, I would like to offer a few:

I think an excellent place to start on the topic you are looking for is George Sansom's A History of Japan 1334-1615. It starts with the conflicts of the early 14th century, which saw the rise of the Ashikiga bakufu, and moves through the sengoku period, up to the Siege of Osaka castle. This is a great place to start because it provides a cohesive narrative on the rise and fall of the Ashikaga shogunate. It also provides a bit more info on the socio-political underpinnings of the period than you would expect from an introductory read, while at the same time giving an engaging and informative account. I would be remiss not to mention that the book was published in the 1960s, so there are parts that are can be a bit dated, but still think its an excellent read, on precisely what you are looking for.

Another book that you might be interested in is Paul Varley's The Ōnin War. This book is often considered to be the go-to English language book on the Ōnin War. As many people hold the Ōnin War as the event which saw the decline of the Ashikiga bakufu (the truth of the matter is much more complicated), its history will be of particular interest to you. I also recommend this book because a large portion of it (about half the book itself) details the history of the Ashikaga prior to the Ōnin War itself, and provides the context to its decline. It is a bit more academic a read than George Sansom's book, so you might not want to use it as a nice follow up, getting you deeper into the topic as a whole.

If you wish to look deeper into the topic, The Cambridge History of Japan Vol 3: Medieval Japan is extremely informative. It is a book with a collection of writings from different authors/historians, each focusing on a different topic relating to the time period. They are very focused works that explore details and conditions had immense effects on the events of the time period. Some individual pieces within the book that will be of interest to the topic are: The Muromachi bakufu by John Whitney Hall, Muromachi local government: shugo and kokujin by Imatani Akira / translated by Suzanne Gay, and The Decline of the shōen system (an occurrence which has a profound relation with the status of the Ashikaga bakufu) by Nagahara Keiji / translated by Michael Birt. This book does not provide a cohesive narrative of the series, and at times is very dense, but as a follow up book, would provide a whole other level of understanding on whats driving the events surrounding the Ashikaga.

Hope that these help. If you are looking for further recommendations, or have any questions, feel free to ask!

Hi there!

We flaired users here at /r/AskHistorians have compiled and maintain a booklist. I suspect, given your question, that the Japan section will be of interest to you. You may want to especially check out this sub-section of that list.

Cheers!