ABSTRACT

In this talk, we introduce a new type of variational problem without any ellipticity or monotonicity condition. A prototype is a differential inclusion whose driving operator is the competing weighted $(p,q)$-Laplacian $- \Delta_p u+\mu\Delta_q u$ with $\mu\in\mathbb{R}$. Local and nonlocal boundary value problems fitting into this nonstandard setting are examined.