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Existence of Positive Solutions of Variational Inequalities by a Subsolution-Supersolution Approach

✍ Scribed by Vy Khoi Le

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 165 KB
Volume: 252
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.6907

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✦ Synopsis

This paper is about the existence of positive solutions and maximalr minimal solutions for a class of quasi-linear noncoercive equations and variational inequalities. Our main tool is a sub-supersolution method for w x inequalities, based on the discussions in 17 . We established in that paper Ž . the existence of solutions and extremal i.e., maximal or minimal solutions of inequalities provided subsolutions andror supersolutions, defined in an appropriate manner, exist. However, the existence and construction of sub-supersolutions are usually nontrivial and depend on the particular problems we are looking for solutions. Our goal here is a construction of sub-and supersolutions for quasi-linear variational inequalities of the form ¡ py 2 < < ٌu ٌu и ٌ ¨y u dx G F x, u, ٌu ¨y u dx, ᭙¨g K

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