13,543 research outputs found
Generalized quasi-variational-like inequality problem
This paper gives
some
very general
results on the
generalized quasi-variational-like
inequality problem.
Since the
problem includes all the
existing
extensions of the classical
variational
inequality problem as
special cases,
our existence theorems extend the
previous
results in the literature
by relaxing
both
continuity
and
concavity
of the functional. The
approach adopted
in this
paper
is based on continuous
selection-type arguments
and thus is
quite
different from the
Berge Maximum Theorem or Hahn-Banach Theorem approach
used
in the literature
Generalized quasi-variational-like inequality problem
This paper gives
some
very general
results on the
generalized quasi-variational-like
inequality problem.
Since the
problem includes all the
existing
extensions of the classical
variational
inequality problem as
special cases,
our existence theorems extend the
previous
results in the literature
by relaxing
both
continuity
and
concavity
of the functional. The
approach adopted
in this
paper
is based on continuous
selection-type arguments
and thus is
quite
different from the
Berge Maximum Theorem or Hahn-Banach Theorem approach
used
in the literature
On the Two Obstacles Problem in Orlicz-Sobolev Spaces and Applications
We prove the Lewy-Stampacchia inequalities for the two obstacles problem in
abstract form for T-monotone operators. As a consequence for a general class of
quasi-linear elliptic operators of Ladyzhenskaya-Uraltseva type, including
p(x)-Laplacian type operators, we derive new results of
regularity for the solution. We also apply those inequalities to obtain new
results to the N-membranes problem and the regularity and monotonicity
properties to obtain the existence of a solution to a quasi-variational problem
in (generalized) Orlicz-Sobolev spaces
Including Social Nash Equilibria in Abstract Economies
We consider quasi-variational problems (variational problems having constraint sets depending on their own solutions) which appear in concrete economic models such as social and economic networks, financial derivative models, transportation network congestion and traffic equilibrium. First, using an extension of the classical Minty lemma, we show that new upper stability results can be obtained for parametric quasi-variational and linearized quasi-variational problems, while lower stability, which plays a fundamental role in the investigation of hierarchical problems, cannot be achieved in general, even on very restrictive conditions. Then, regularized problems are considered allowing to introduce approximate solutions for the above problems and to investigate their lower and upper stability properties. We stress that the class of quasi-variational problems include social Nash equilibrium problems in abstract economies, so results about approximate Nash equilibria can be easily deduced.quasi-variational, social Nash equilibria, approximate solution, closed map, lower semicontinuous map, upper stability, lower stability
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