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Nonlinear variational inequalities on convex subsets of Banach spaces. (English) Zbl 0905.47055
The author proves existence results for solutions of variational inequalities involving so-called $p$-monotone operators.

##### MSC:
 47J20 Inequalities involving nonlinear operators 49J40 Variational methods including variational inequalities 47H05 Monotone operators (with respect to duality) and generalizations
Full Text:
##### References:
 [1] Browder, F. E.: Nonlinear monotone operators and convex sets in Banach spaces. Bull. amer. Math. soc. 71, 780-785 (1965) · Zbl 0138.39902 [2] D. Goeleven and D. Motreanu, Eigenvalue and dynamic problems for variational and hemivarational inequalities, Commun. Appl. Nonlinear Anal. (to appear). · Zbl 0911.49009 [3] Glowinski, R.: Numerical methods for nonlinear variational problems. (1984) · Zbl 0536.65054 [4] Glowinski, R.; Lions, J. L.; Tremolieres, R.: Numerical analysis of variational inequalities. (1981) · Zbl 0463.65046 [5] Kinderlehrer, D.; Stampacchia, G.: An introduction to variational inequalities and their applications. (1980) · Zbl 0457.35001 [6] Szulkin, A.: Positive solutions of varational inequalities: A degree-theoretic approach. J. diff. Eqn. 57, 90-111 (1985) · Zbl 0535.35029 [7] Verma, R. U.: Nonlinear variational and constrained hemivarational inequalities involving relaxed operators. Zamm 77, No. 5, 387-391 (1997) · Zbl 0886.49006 [8] Yao, J. C.: Applications of variational inequalities to nonlinear analysis. Appl. math. Lett. 4, No. 4, 89-92 (1991) · Zbl 0734.49003