A new class of Caffarelli-Kohn-Nirenberg type differential inclusion problems with singular terms and multivalued convection

Abstract

The present article focuses on the research of a new kind of Caffarelli-Kohn-Nirenberg type differential inclusion problems (CKNDI, for short) involving a singular perturbation and a multivalued convection term. We develop a new framework by combining the super-sub solutions method, truncation techniques and the theory of multivalued pseudomonotone operators, to prove the existence of a positive solution to our class of problems.