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2 results

  • TWO NONTRIVIAL WEAK SOLUTIONS FOR THE DIRICHLET PROBLEM ON THE SIERPIŃSKI GASKET

  • Part of
  • DENISA STANCU-DUMITRU
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 85 / Issue 3 / June 2012
    Published online by Cambridge University Press:
    12 December 2011, pp. 395-414
    Print publication:
    June 2012
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  • We study a Dirichlet problem involving the weak Laplacian on the Sierpiński gasket, and we prove the existence of at least two distinct nontrivial weak solutions using Ekeland’s Variational Principle and standard tools in critical point theory combined with corresponding variational techniques.

  • OPTIMAL CONTROL PROBLEMS FOR GENERAL GLOBAL HYBRID DYNAMICAL SYSTEMS WITH MATRIX COST FUNCTIONAL

  • Part of
  • RUI GAO, XINZHI LIU
  • Journal:
    The ANZIAM Journal / Volume 51 / Issue 3 / January 2010
    Published online by Cambridge University Press:
    04 October 2010, pp. 331-349
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  • This paper considers an optimal control problem for a class of controlled hybrid dynamical systems (HDSs) with prescribed switchings. By using Ekeland’s variational principle and a matrix cost functional, a minimum principle for HDSs is derived, which provides a necessary condition of the aforementioned problem. The results given in this paper include both pure continuous systems and pure discrete-time systems as special cases.