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2004•Georgian Mathematical JournalRequires access

On the Uniqueness of Solutions of Some Quasi-Variational Inequalities from Control Theory

Avtandil Gachechiladze

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Abstract

The existence and uniqueness problems for some quasi-variational inequalities are studied on the basis of the L ∞ -estimates for solutions of the variational inequalities and their differences. An implicit obstacle problem is stated by analogy with one quasi-variational inequality studied by Benoussan and Lions (Méthodes Mathématiques de l'Informatique 11: 1982) and Vescan (1982) and its unique solvability is proved. Some conclusions are given concerning the uniqueness of solutions for an impulse control problem with bilateral restrictions and for a quasi-variational inequality appearing in dynamic programming.

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The existence and uniqueness problems for some quasi-variational inequalities are studied on the basis of the L ∞ -estimates for solutions of the variational inequalities and their differences. An implicit obstacle problem is stated by analogy with one quasi-variational inequality studied by Benoussan and Lions (Méthodes Mathématiques de l'Informatique 11: 1982) and Vescan (1982) and its unique solvability is proved. Some conclusions are given concerning the uniqueness of solutions for an impulse control problem with bilateral restrictions and for a quasi-variational inequality appearing in dynamic programming.

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Available abstract

The existence and uniqueness problems for some quasi-variational inequalities are studied on the basis of the L ∞ -estimates for solutions of the variational inequalities and their differences. An implicit obstacle problem is stated by analogy with one quasi-variational inequality studied by Benoussan and Lions (Méthodes Mathématiques de l'Informatique 11: 1982) and Vescan (1982) and its unique solvability is proved. Some conclusions are given concerning the uniqueness of solutions for an impulse control problem with bilateral restrictions and for a quasi-variational inequality appearing in dynamic programming.

Key concepts: Uniqueness, Variational inequality, Mathematics, Obstacle, Obstacle problem, Inequality, Applied mathematics, Analogy

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