Displaying similar documents to “Existence results for quasi variational inequalities.”

On some variational inequalities for nonclassical type operators

Sergey Glazatov (1992)

Banach Center Publications

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The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.

Monotonicity properties of minimizers and relaxation for autonomous variational problems

Giovanni Cupini, Cristina Marcelli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the following classical autonomous variational problem minimize F ( v ) = ∫ a b f ( v ( x ) , v ' ( x ) ) x ̣ : v ∈ A C ( [ a , b ] ) , v ( a ) = α , v ( b ) = β , where the Lagrangianf is possibly neither continuous, nor convex, nor coercive. We prove a monotonicity property of the minimizers stating that they satisfy the maximum principle or the minimum one. By virtue of such a property, applying recent results concerning constrained variational problems, we derive a relaxation theorem, the DuBois-Reymond necessary condition...

A Recession Notion for a Class of Monotone Bivariate Functions

Moudafi, A. (2000)

Serdica Mathematical Journal

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Using monotone bifunctions, we introduce a recession concept for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on variational problems. In the process we generalize some results by H. Brezis and H. Attouch relative to the convergence of the resolvents associated with maximal monotone operators.