Chen, Yu-Qing On the semi-monotone operator theory and applications. (English) Zbl 0934.47031 J. Math. Anal. Appl. 231, No. 1, 177-192 (1999). The author studies a variational inequality governed by a semi-monotone operator and develops a degree theory for demicontinuous semi-monotone operators in reflexive Banach spaces. Reviewer: I.Vrabie (Iaşi) Cited in 3 ReviewsCited in 34 Documents MSC: 47H05 Monotone operators and generalizations 47J20 Variational and other types of inequalities involving nonlinear operators (general) 47H11 Degree theory for nonlinear operators 35J50 Variational methods for elliptic systems Keywords:variational inequality; degree theory; demicontinuous semi-monotone operators PDFBibTeX XMLCite \textit{Y.-Q. Chen}, J. Math. Anal. Appl. 231, No. 1, 177--192 (1999; Zbl 0934.47031) Full Text: DOI References: [1] Aizicovici, S.; Chen, Y. Q., Note on the topological degree of the subdifferential of a lower semi-continuous convex function, Proc. Amer. Math. Soc., 126, 2905-2908 (1998) · Zbl 0903.47036 [2] Barbu, V., Nonlinear Semigroups and Differential Equations in Banach Spaces (1976), Noordhoff [3] Browder, F. E., Semicontractive and semiaccretive nonlinear mappings in Banach space, Bull. Amer. Math. Soc., 74, 660-665 (1968) · Zbl 0164.44801 [4] Browder, F. E., Nonlinear Operators and Nonlinear Equations of Evolutions in Banach Spaces, Proc. Symp. Pure Math., 18 (1976) · Zbl 0176.45301 [5] Browder, F. E., Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc., 1, 1-39 (1983) · Zbl 0533.47053 [6] Chang, S. S.; Lee, B. S.; Chen, Y. Q., Variational inequalities for monotone operators in nonreflexive Banach spaces, Appl. Math. Lett., 8, 29-34 (1995) · Zbl 0840.47052 [7] Chen, Y. Q., On accretive operators in cones of Banach spaces, Non. Anal., 27, 1125-1135 (1996) · Zbl 0883.47057 [8] Chipot, M., Variational Inequalities and Flow in Porous Media (1984), Springer-Verlag: Springer-Verlag Berlin · Zbl 0544.76095 [9] Deimling, K., Nonlinear Functional Analysis (1984), Springer-Verlag: Springer-Verlag Berlin [10] Duvaut, G.; Lions, J. L., Les Inequations en Mecanique et en Physique (1970), Dunod · Zbl 0298.73001 [11] Gossez, J. P., Operateurs monotones nonlineaires dans les espaces de Banach nonreflexifs, J. Math. Anal. Appl., 34, 371-395 (1971) · Zbl 0228.47040 [12] Guo, J. S.; Yao, J. C., Variational inequalities with nonmonotone operators, J. Optim. Theory Appl., 80, 63-74 (1994) · Zbl 0798.49013 [13] Hartman, P.; Stampacchia, G., On some nonlinear elliptic differential functional equations, Acta Math., 115, 271-310 (1966) · Zbl 0142.38102 [14] Kinderlehrer, D.; Stampacchia, G., An Introduction to Variational Inequalities and Their Applications (1980), Academic: Academic New York · Zbl 0457.35001 [15] Krasnoselskii, M. A., Two remarks on the method of successive approximations, Uspehi Mat. Nauk., 10, 123-127 (1955) [16] Minty, G. J., On the generalization of a direct method of calculus of variations, Bull. Amer. Math. Soc., 73, 315-321 (1967) · Zbl 0157.19103 [17] Nirenberg, L., Topics in Nonlinear Functional Analysis. Topics in Nonlinear Functional Analysis, Lecture Notes (1974), Courant Institute · Zbl 0286.47037 [18] Nirenberg, L., Variational and topological methods in nonlinear problems, Bull. Amer. Math. Soc., 4, 267-302 (1981) · Zbl 0468.47040 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.