J4 ›› 2013, Vol. 51 ›› Issue (01): 92-93.

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Extremal Problems of Partial Differential Inclusions

CHENG Yi1,2, HUA Hongtu2, LI Qiuyue2   

  1. 1. Institute of Mathematics, Jilin University, Changchun 130012, China;
    2. Department of Foundation, Aviation University of Air Force, Changchun 130022, China
  • Received:2012-05-21 Online:2013-01-26 Published:2013-01-31
  • Contact: CHENG Yi E-mail:chengyi407@126.com

Abstract:

This paper deals with the boundary value problems for a class of partial differential inclusions -Δ u∈ext G(x,u). When 
G(x,u) takes bounded, weakly compact, convex values, and is measurable about variable x, is continuous about variable u, we proved the existence of extremal solutions on the basis of Tolstonogov extremal continuous selection theorem.

Key words: partial differential inclusion, extremal solution, fixed point

CLC Number: 

  • O175.14