Well-posedness without semicontinuity for parametric quasiequilibria and quasioptimization

Well-Posedness Under Relaxed Semicontinuity for Bilevel Equilibrium and Optimization Problems with Equilibrium Constraints

Bilevel equilibrium and optimization problems with equilibrium constraints are considered. We propose a relaxed level closedness and use it together with pseudocontinuity assumptions to establish sufficient conditions for well-posedness and unique well-posedness. These conditions are new even for problems in onedimensional spaces, but we try to prove them in general settings. For problems in to...

Well-posedness for Parametric Vector Equilibrium Problems with Applications

In this paper, we study the parametric well-posedness for vector equilibrium problems and propose a generalized well-posed concept for equilibrium problems with equilibrium constraints (EPEC in short) in topological vector spaces setting. We show that under suitable conditions, the well-posedness defined by approximating solution nets is equivalent to the upper semicontinuity of the solution ma...

Lower semicontinuity for parametric set-valued vector equilibrium-like problems

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...

Well-posedness for Hall-magnetohydrodynamics

We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resitive, viscous or inviscid Hall-MHD model. We also show a Liouville theorem for the stationary solutions. Acknowledgements: The first and third authors wish to thank the hospitality of the Institut de Mathématiques de Toulouse, France, where this research has been car...

Well-posedness for Hyperbolic Problems