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@ARTICLE{,
    author = {Bensoussan, Alain and Bul{\'{\i}}{\v c}ek, Miroslav and Frehse, Jens},
  keywords = {Bellman equation, Hamiltonians, nonlinear elliptic equations, renor- malized sub- and super-solutions., Stochastic games, weak lower- and upper- stability, weak solution},
     title = {Existence and compactness for weak solutions to Bellman systems with critical growth},
   journal = {Discrete and Continuous Dynamical Systems - Series B},
    volume = {17},
    number = {6},
      year = {2012},
     pages = {1729--1750},
      note = {Preprint NCMM No 2011-012},
       url = {http://www.karlin.mff.cuni.cz/ncmm/preprints/11129153006pr12.pdf},
       doi = {10.3934/dcdsb.2012.17.1729},
  abstract = {We deal with nonlinear elliptic and parabolic systems
that are the Bellman systems associated to stochastic dierential
games as a main motivation. We establish the existence of weak
solutions in any dimension for an arbitrary number of equations
(\players"). The method is based on using a renormalized sub-
and super-solution technique. The main novelty consists in the
new structure conditions on the critical growth terms with allow
us to show weak solvability for Bellman systems to certain classes
of stochastic dierential games.}
}