On variational inequalities with maximal monotone operators and multivalued perturbing terms in Sobolev spaces with variable exponents. (English) Zbl 1234.47046
The purpose of this paper is to prove the existence of solutions of variational inequalities with maximal monotone operators and multivalued perturbing terms in Sobolev spaces with variable exponents, and to study both coercive and noncoercive inequalities. In the noncoercive case, a sub-supersolution approach is followed to obtain the existence and some other qualitative properties of solutions between sub- and supersolutions. The results presented in this paper improve and extend many known results in the recent literature.
Reviewer: Hengyou Lan (Zigong)
MSC:
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 49J40 | Variational inequalities |
| 90C31 | Sensitivity, stability, parametric optimization |
| 47H05 | Monotone operators and generalizations |
| 47E05 | General theory of ordinary differential operators |
Keywords:
variational inequalities; nonlinear operators; sensitivity; stability; monotone operators; ordinary differential operatorsReferences:
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