References
Aggeri, J. C., etC. Lescarret: Sur une application de la théorie de la sous-differentiabilité à des fonctions convexes duales associés à un couple d'ensembles mutuellement polaires. (Mimeographed manuscript.) Montpellier 1965.
Asplund, E.: Positivity of duality mappings. Bull Am. Math. Soc.73, 200–203 (1967).
Beurling, A., andA. E. Livingston: A theorem on duality mappings in Banach spaces. Ark. Math.4, 405–411 (1961).
Bronsted, A., andR. T. Rockafellar: On the subdifferentiability of convex functions. Proc. Am. Math. Soc.16, 605–611 (1965).
Browder, F. E.: Nonlinear elliptic boundary value problems. Bull. Am. Math. Soc.69, 862–874 (1963).
——: Nonlinear elliptic problems, II. Bull. Am. Math. Soc.70, 299–302 (1964).
—— Strongly nonlinear parabolic boundary value problems. Am. J. Math.86, 339–357 (1964).
—— Nonlinear elliptic boundary value problems, II. Trans. Am. Math. Soc.117, 530–550 (1965).
—— Nonlinear equations of evolution. Ann. Math.80, 485–523 (1964).
—— On a theorem of Beurling and Livingston. Canad. J. Math.17, 367–372 (1965).
—— Multivalued monotone nonlinear mappings and duality mappings in Banach spaces. Trans. Am. Math. Soc.118, 338–351 (1965).
—— Continuity properties of monotone nonlinear operators in Banach spaces. Bull. Am. Math. Soc.70, 551–553 (1964).
—— Nonlinear initial value problems. Ann. Math.82, 51–87 (1965).
—— Nonlinear monotone operators and convex sets in Banach spaces. Bull. Am. Math. Soc.71, 780–785 (1965).
—— Existence and uniqueness theorems for solutions of nonlinear boundary value problems. Proc. Symposia on Appl. Math., Am. Math. Soc.17, 24–49 (1965).
—— Mapping theorems for noncompact nonlinear operators in Banach spaces. Proc. Nat. Acad. Sci. U.S.54, 337–342 (1965).
—— Nonlinear functional equations in nonreflexive Banach spaces. Bull. Am. Math. Soc.72, 89–95 (1966).
-- Problèmes nonlinéaires. 153 pp. Univ. of Montreal Press 1966.
—— On the unification of the calculus of variations and the theory of monotone nonlinear operators in Banach spaces. Proc. Nat. Acad. Sci. U.S.56, 419–425 (1966).
—— Existence and approximation of solutions of nonlinear variational inequalities. Proc. Nat. Acad. Sci. U.S.56, 1080–1086 (1966).
Hartman, P., andG. Stampacchia: On some nonlinear elliptic functional differential equations. Acta. Math.115, 271–310 (1966).
Kacurovski, R. I.: On monotone operators and convex functionals. Usp. Mat. Nauk.15, 213–215 (1960).
Kato, T.: Demicontinuity, hemicontinuity, and monotonicity. Bull. Am. Math. Soc.70, 548–550 (1964).
—— Nonlinear equations of evolution in Banach spaces. Symposia on Appl. Math., Am. Math. Soc.17, 50–67 (1965).
Leray, J., etJ. L. Lions: Quelques resultats de Visik sur les problemes elliptiques nonlinéaires par les methodes de Minty-Browder. Bull. soc. math. France93, 97–107 (1965).
Lescarret, C.: Cas d'addition des applications monotones maximales dans un espace de Hilbert. Compt. Rend.261, 1160–1163 (1965).
Lions, J. L., etG. Stampacchia: Inequations variationelles noncoercives. Compt. Rend.261, 25–27 (1965).
-- Variational inequalities. (To appear.)
Minty, G. J.: Monotone (nonlinear) operators in Hilbert space. Duke Math. J.29, 341–346 (1962).
——: On the monotonicity of the gradient of a convex function. Pacific. J. Math.14, 243–247 (1964).
—— On a “monotonicity” method for the solution of nonlinear equations in Banach spaces. Proc. Nat. Acad. Sci. U.S.50, 1038–1041 (1963).
—— A theorem on maximal monotonic sets in Hilbert spaces. J. Math. Anal. and Appl.11, 434–439 (1965).
—— On the generalization of the direct method of the calculus of variations. Bull. Am. Math. Soc.73, 315–321 (1967).
Moreau, J. J.: Fonctionelles sous-differentiables. Compt. Rend.257, 4117–4119 (1963).
—— Proximité et dualité dans un éspace hilbertien. Bull. soc. math. France93, 273–299 (1965).
Rockafellar, R. T.: Characterization of the subdifferentials of convex functions. Pacific J. Math.17, 497–510 (1966).
Stampacchia, G.: Formes bilinéaires coercitives sur les ensembles convexes. Comt. Rend.258, 4413–4416 (1964).
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Browder, F.E. Nonlinear maximal monotone operators in Banach space. Math. Ann. 175, 89–113 (1968). https://doi.org/10.1007/BF01418765
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DOI: https://doi.org/10.1007/BF01418765