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A variational inequality index for condensing maps in Hilbert spaces and applications to semilinear elliptic inequalities

โœ Scribed by K.Q. Lan; W. Lin

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
271 KB
Volume
74
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

A variational inequality index for ฮณ -condensing maps is established in Hilbert spaces. New results on existence of nonzero positive solutions of variational inequalities for such maps are proved by using the theory of variational inequality index. Applications of such a theory are given to existence of nonzero positive weak solutions for semilinear second order elliptic inequalities, where previous results of variational inequalities for S-contractive maps cannot be applied.

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Recently, Ceng, Guu and Yao introduced an iterative scheme by viscosity-like approximation method to approximate the fixed point of nonexpansive mappings and solve some variational inequalities in Hilbert space (see Ceng et al. (2009) [9]). Takahashi and Takahashi proposed an iteration scheme to sol