In the case of animals it is not common to refer to mental disorders, there is more commonly talked about behavior problems, (it is not specified in the question what kind of animals) although in essence animals can suffer the same as a human, sometimes the variations are huge, depends on which type of animal we refer (it is not the same to speak of chimpanzee or bonobo than of mammals or other animals).
Here are some examples of psychology (about mammals) that may be of interest, are nowadays sensitive and may even surprise some (OCD, bipolar, dementia, autism, Alzheimer, etc.).
(Ethology is the science that is responsible for the study of animal behavior, although it is not the only science that studies it, for example, in the studies of psychology there are 2 subjects in relation to animal behavior: biology that sometimes It is administered by an ethologist, and comparative psychology, the latter can receive different denominations in different countries. Professionals in charge of therapy and / or training vary widely depending on the country, some are: ethologists, veterinarians, trainers but there are many more).
- MOTOR DISORDERS, STEREOTYPIES AND OCD:
In many cases animals are found with what some people classify as motor behavior disorders, other considerations can lead to obsessive compulsive disorders. These problems may consist of a bird that can no longer fly, a dog that stores objects of a certain characteristic (without food function); or a dog that usually turns and turns on itself. These problems can be caused by restrictions on movement, for example not letting a bird fly or not respecting the bird's flight practice (there are others that are produced by the way of life and hormones).
Examples of stereotypy at the beginning of the video, Chimpance raised with artificial mother without movement and children orphaned in institutions: https://www.youtube.com/watch?v=H6sKo-OKAuE
- ANXIETY AND POSTTRAUMATIC STRESS:
It is well known that dogs can develop post-traumatic stress following environmental catastrophes, for example it is well known that after floods and earthquakes many times dogs experience anxiety and flashbacks.
Of course the animals can experience stress due to mistreatment.
Interesting links: https://www.cesarsway.com/dog-behavior/anxiety/post-traumatic-stress-disorder https://www.cesarsway.com/dog-behavior/anxiety/veteran-dogs-suffering-from-ptsd
- SYSTEMATIZED PROBLEMS (DISORDES) DEVELOPDEP BY LEARNING, great variety.
Attachment and sociability: See Harlow experiments.
Aggressiveness. Today there is widespread debate about aggressive behavior resulting from mistreatment.
Depression / defenselessness learned. No doubt the animals have emotions, in their case not usually considered depression but learned helplessness, see Seligman experiments, also Seligman and Maier.
An article I have found about it and may be interesting as well as being related to the question, but many others may be found: https://www.researchgate.net/profile/Isabelle_Veissier/publication/230851712_Animals'_emotions_Studies_in_sheep_using_appraisal_theories/links/09e41505478be19677000000/Animals-emotions-Studies-in-sheep-using-appraisal-theories.pdf
Of course: https://books.google.com/books?hl=en&lr=&id=kc3CAgAAQBAJ&oi=fnd&pg=PP1&dq=animals+emotions&ots=s1J20NZ2u7&sig=Jc-MAGzmDwPMwb-WWVIlJ1z8TFo#v=onepage&q=animals%20emotions&f=false
- ORGANIC DISORDERS, an incredible broad field, some examples:
Patterson, P.H. (2009). Immune involvement in schizophrenia and autism: etiology, pathology and animal models. Behav. Brain Res. 204, 313–321.
Müller, M.B. & Holsboer, F. (2006). Mice with mutations in the HPA-system as models for symptoms of depression. Biol. Psychiatry 59, 1104–1115.
Götz, J. & Ittner, L.M. (2008) Animal models of Alzheimer's disease and frontotemporal dementia. Nat. Rev. Neurosci. 9, 532–544.
Jamain, S. (2008). Reduced social interaction and ultrasonic communication in a mouse model of monogenic heritable autism. Proc. Natl. Acad. Sci. USA 105, 1710–1715. Moy, S.S. & Nadler, J.J. (2008). Advances in behavioral genetics: mouse models of autism. Mol. Psychiatry 13, 4–26.
Einat, H. & Manji, H.K. (2006). Cellular plasticity cascades: genes-to-behavior pathways in animal models of bipolar disorder. Biol. Psychiatry 59, 1160–1171