Note on the topological degree of the subdifferential of a lower semi-continuous convex function
HTML articles powered by AMS MathViewer
- by Sergiu Aizicovici and Yuqing Chen PDF
- Proc. Amer. Math. Soc. 126 (1998), 2905-2908 Request permission
Abstract:
The purpose of the present paper is to prove that the topological degree of the subdifferential of a coercive lower semi-continuous function on a sufficiently large ball in a reflexive Banach space is equal to one.References
- Herbert Amann, A note on degree theory for gradient mappings, Proc. Amer. Math. Soc. 85 (1982), no. 4, 591–595. MR 660610, DOI 10.1090/S0002-9939-1982-0660610-2
- H. Attouch, Variational convergence for functions and operators, Applicable Mathematics Series, Pitman (Advanced Publishing Program), Boston, MA, 1984. MR 773850
- Juha Berkovits and Vesa Mustonen, On the topological degree for mappings of monotone type, Nonlinear Anal. 10 (1986), no. 12, 1373–1383. MR 869546, DOI 10.1016/0362-546X(86)90108-2
- Felix E. Browder, Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc. (N.S.) 9 (1983), no. 1, 1–39. MR 699315, DOI 10.1090/S0273-0979-1983-15153-4
- Felix E. Browder, Degree theory for nonlinear mappings, Nonlinear functional analysis and its applications, Part 1 (Berkeley, Calif., 1983) Proc. Sympos. Pure Math., vol. 45, Amer. Math. Soc., Providence, RI, 1986, pp. 203–226. MR 843560
- Shi Sheng Zhang and Yu-chin Chen, Degree theory for multivalued $(S)$-type mappings and fixed-point theorems, Appl. Math. Mech. 11 (1990), no. 5, 409–421 (Chinese, with English summary); English transl., Appl. Math. Mech. (English Ed.) 11 (1990), no. 5, 441–454. MR 1069804, DOI 10.1007/BF02016374
- M. A. Krasnosel’skii, Topological methods in the theory of nonlinear integral equations, A Pergamon Press Book, The Macmillan Company, New York, 1964. Translated by A. H. Armstrong; translation edited by J. Burlak. MR 0159197
- L. Nirenberg, Variational and topological methods in nonlinear problems, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 3, 267–302. MR 609039, DOI 10.1090/S0273-0979-1981-14888-6
- Paul H. Rabinowitz, A note on topological degree for potential operators, J. Math. Anal. Appl. 51 (1975), no. 2, 483–492. MR 470773, DOI 10.1016/0022-247X(75)90134-1
- Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
- James C. Scovel, A simple intuitive proof of a theorem in degree theory for gradient mappings, Proc. Amer. Math. Soc. 93 (1985), no. 4, 751–753. MR 776215, DOI 10.1090/S0002-9939-1985-0776215-1
- S. L. Trojansky, On locally uniformly convex and differentiable norms in certain nonseparable Banach spaces, Studia Math., 37(1971), 173-180.
Additional Information
- Sergiu Aizicovici
- Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701-2979
- Email: aizicovi@bing.math.ohiou.edu
- Yuqing Chen
- Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701-2979
- Email: yuqchen@bing.math.ohiou.edu
- Received by editor(s): February 25, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2905-2908
- MSC (1991): Primary 47H10, 47H15; Secondary 55M25
- DOI: https://doi.org/10.1090/S0002-9939-98-04529-8
- MathSciNet review: 1468179