On the Existence of a Generalized Solution of One Partial Differential System - Solonukha, O.V. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
We propose a method for the construction of generalized solutions for some nondivergent partial differential systems using set-valued analogs of the generalized statement of the problem based on subdifferential calculus. We establish new sufficient conditions for the existence of solutions of a variational inequality with set-valued operator under weakened coerciveness conditions. We consider examples of a weighted p-Laplacian in the Sobolev spaces \(W_p^1 ( Ω )\) , p ≥ 2.