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.
Su, G., Vetro, C., Zeng, S., Zhong, Z. (2026). A new class of Caffarelli-Kohn-Nirenberg type differential inclusion problems with singular terms and multivalued convection. COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION, 152(Part B), 1-10 [10.1016/j.cnsns.2025.109209].
A new class of Caffarelli-Kohn-Nirenberg type differential inclusion problems with singular terms and multivalued convection
Vetro C.;
2026-01-01
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.
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