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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
Article
  • 17 Downloads

Abstract

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.

Keywords

Generalize Statement Generalize Solution Variational Inequality Sobolev Space Differential System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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