The goal of this note is to present different uniqueness results for problems associated with pseudo-monotone operators having the structure of the p -Laplace operator. The results are quite different when the equations at hand have a strictly monotone lower order term. The topic uses different test functions depending on the assumptions of the coefficients of the operators. Some of them are used in the references mentioned below but most of the time we simplify them and compare their strength. At the end of the note, we introduce some new type of such operators for which uniqueness can be proved roughly speaking the same way. MSC2020-Mathematics Subject Classification: 35A16, 35J60, 35J66, 35J92.
Michel Chipot (Thu,) studied this question.