Ukrainian Mathematical Journal

, Volume 54, Issue 9, pp 1509–1525 | Cite as

On the Existence of a Generalized Solution of One Partial Differential System

  • O. V. Solonukha


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.


Generalize Statement Generalize Solution Variational Inequality Sobolev Space Differential System 
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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • O. V. Solonukha
    • 1
  1. 1.“KPI” National Technical UniversityKiev

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