On the Existence of a Generalized Solution of One Partial Differential System
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 \(W_p^1 \left( \Omega \right)\) , p ≥ 2.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 9, pp 1509-1525.
Citation Example: Solonukha O.V. On the Existence of a Generalized Solution of One Partial Differential System // Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1250-1264.