Note on the topological degree

of the subdifferential

of a lower semi-continuous convex function

Authors:
Sergiu Aizicovici and Yuqing Chen

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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**1.**H. Amann, A note on degree theory for gradient mappings, Proc. Amer. Math. Soc., 85(1982),591-595. MR**83i:47069****2.**H. Attouch, Variational Convergence for Functions and Operators, Pitman,Boston,1984. MR**86f:49002****3.**J. Berkovits and V. Mustonen, On the degree for mappings of monotone type, Nonlinear Anal., 12(1986),1373-1383. MR**88b:47073****4.**F.E.Browder, Fixed point theory and nonlinear problems, Bull.Amer.Math. Soc., 1(1983),1-39. MR**84h:58027****5.**F.E.Browder, Degree theory for nonlinear mappings, Proc. Symp.Pure Math., Vol.45,pp.203-226, Amer.Math.Soc., Providence,R.I., 1986. MR**87g:47108****6.**Y.Q. Chen and S. S. Zhang, Degree theory for multivalued (S) type mappings and fixed point theorems, Applied Math.Mech., English Ed., 11(1990),441-454. MR**91h:47065****7.**M.A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations,Macmillan, New York,1964. MR**28:2414****8.**L. Nirenberg, Variational and topological methods in nonlinear problems, Bull. Amer. Math. Soc., 4(1981),267-302. MR**83e:58015****9.**P. H. Rabinowitz, A note on topological degree for potential operators, J. Math. Anal. Appl., 51(1975),483-492. MR**57:10518****10.**E. H. Rothe, A relation between the type numbers of a critical point and the index of the corresponding field of gradient vectors, Math. Nachr., 4(1950-51), 12-17. MR**12:720c****11.**J. C. Scovel, A simple intuitive proof of a theorem in degree theory for gradient mappings, Proc. Amer. Math. Soc., 93(1985), 751-753. MR**86g:55001****12.**S. L. Trojansky, On locally uniformly convex and differentiable norms in certain nonseparable Banach spaces, Studia Math., 37(1971), 173-180.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
47H10,
47H15,
55M25

Retrieve articles in all journals with MSC (1991): 47H10, 47H15, 55M25

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

DOI:
https://doi.org/10.1090/S0002-9939-98-04529-8

Keywords:
Monotone operator,
class $(S_+)$,
topological degree

Received by editor(s):
February 25, 1997

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society