Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 13, Number 2 (2019), 293-313.
On the existence of solutions of variational inequalities in nonreflexive Banach spaces
We are concerned in this article with an existence theorem for variational inequalities in nonreflexive Banach spaces with a general coercivity condition. The variational inequalities contain multivalued generalized pseudomonotone mappings and convex functionals, the nonreflexive Banach spaces form a complementary system, and the coercivity condition involves both the mapping and the functional. As an application, we study second-order elliptic variational inequalities with multivalued lower-order terms in general Orlicz–Sobolev spaces.
Banach J. Math. Anal., Volume 13, Number 2 (2019), 293-313.
Received: 20 July 2018
Accepted: 13 October 2018
First available in Project Euclid: 28 January 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]
Secondary: 46B10: Duality and reflexivity [See also 46A25] 35J87: Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities [See also 35R35, 49J40] 58E35: Variational inequalities (global problems)
Le, Vy Khoi. On the existence of solutions of variational inequalities in nonreflexive Banach spaces. Banach J. Math. Anal. 13 (2019), no. 2, 293--313. doi:10.1215/17358787-2018-0034. https://projecteuclid.org/euclid.bjma/1548666054