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Journal of Convex Analysis 16 (2009), No. 3, 899--911
Copyright Heldermann Verlag 2009



On Existence Theorems for Monotone and Nonmonotone Variational Inequalities

Antonino Maugeri
Dip. di Matematica e Informatica, UniversitÓ di Catania, Viale A. Doria 6-I, 95125 Catania, Italy
maugeri@dmi.unict.it

Fabio Raciti
Dip. di Matematica e Informatica, UniversitÓ di Catania, Viale A. Doria 6-I, 95125 Catania, Italy
fraciti@dmi.unict.it



We make a comparison among various existence theorems for monotone and nonmonotone variational inequalities and give necessary conditions for the solvability of the variational inequality problem.

Keywords: Brezis-pseudomonotonicity, Karamardian-pseudomonotonicity, Fan-hemicontinuity, hemicontinuity along line segments, coercivity.

MSC: 47H05, 52A41,39B82

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