Differential and Integral Equations

The sub-supersolution method and extremal solutions for quasilinear hemivariational inequalities

S. Carl, Vy K. Le, and D. Motreanu

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We generalize the sub-supersolution method known for weak solutions of single and multivalued equations to quasilinear elliptic hemivariational inequalities. To this end we first introduce our basic notion of sub- and supersolutions on the basis of which we then prove existence, comparison, compactness, and extremality results for the hemivariational inequalities under considerations.

Article information

Differential Integral Equations, Volume 17, Number 1-2 (2004), 165-178.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J85
Secondary: 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40] 49J40: Variational methods including variational inequalities [See also 47J20]


Carl, S.; Le, Vy K.; Motreanu, D. The sub-supersolution method and extremal solutions for quasilinear hemivariational inequalities. Differential Integral Equations 17 (2004), no. 1-2, 165--178. https://projecteuclid.org/euclid.die/1356060478

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