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Variational inequalities in noncompact nonconvex regions

Ching-Yan Lin, Liang-Ju Chu (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, a general existence theorem on the generalized variational inequality problem GVI(T,C,ϕ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set. Equipped with a kind of V₀-Karamardian condition, this general existence theorem contains some existing ones as special cases. Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem on GVI(T,C,ϕ),...

Variational Principles for Monotone and Maximal Bifunctions

Chbani, Zaki, Riahi, Hassan (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05We establish variational principles for monotone and maximal bifunctions of Brøndsted-Rockafellar type by using our characterization of bifunction’s maximality in reflexive Banach spaces. As applications, we give an existence result of saddle point for convex-concave function and solve an approximate inclusion governed by a maximal monotone operator.

Vector and operator valued measures as controls for infinite dimensional systems: optimal control

N.U. Ahmed (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider a general class of systems determined by operator valued measures which are assumed to be countably additive in the strong operator topology. This replaces our previous assumption of countable additivity in the uniform operator topology by the weaker assumption. Under the relaxed assumption plus an additional assumption requiring the existence of a dominating measure, we prove some results on existence of solutions and their regularity properties both for linear and semilinear...

Vector integral equations with discontinuous right-hand side

Filippo Cammaroto, Paolo Cubiotti (1999)

Commentationes Mathematicae Universitatis Carolinae

We deal with the integral equation u ( t ) = f ( ∫ I g ( t , z ) u ( z ) d z ) , with t ∈ I = [ 0 , 1 ] , f : 𝐑 n → 𝐑 n and g : I × I → [ 0 , + ∞ [ . We prove an existence theorem for solutions u ∈ L ∞ ( I , 𝐑 n ) where the function f is not assumed to be continuous, extending a result previously obtained for the case n = 1 .

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