Publication Cover
Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 13
63
Views
1
CrossRef citations to date
0
Altmetric
Articles

Topological degree for quasibounded multivalued (S̃)+-perturbations of maximal monotone operators

ORCID Icon
Pages 2339-2360 | Received 17 Jul 2018, Accepted 18 Dec 2018, Published online: 01 Jan 2019

References

  • Brézis H, Crandall MG, Pazy A. Perturbations of nonlinear maximal monotone sets in Banach spaces. Comm Pure Appl Math. 1970;23:123–144. doi: 10.1002/cpa.3160230107
  • Pascali D, Sburlan S. Nonlinear mappings of monotone type. Bucharest: Sijthoff and Noordhoof; 1978.
  • Zeidler E. Nonlinear functional analysis and its applications. New York: Springer-Verlag; 1990.
  • Barbu V. Nonlinear semigroups and differential equations in Banach spaces. Leyden (The Netherlands): Noordhoff Int. Publ.; 1975.
  • Browder FE. Nonlinear operators and nonlinear equations of evolution in Banach spaces. Proc Sympos Pure Appl Math. 1976;18. Part 2, Providence, RI.
  • Simons S. Minimax and monotonicity. Vol. #1693. Berlin: Springer-Verlag; 1998. (Lecture Notes in Mathematics).
  • Skrypnik IV. Methods for analysis of nonlinear elliptic boundary value problems. Vol. #139. Providence, RI: American Mathematical Society; 1994. (Amer. Math. Soc. Transl., Ser. II).
  • Lloyd NG. Degree theory. Cambridge: Cambridge Univ. Press; 1978.
  • Fonseca I, Gangbo W. Degree theory in analysis and applications. Oxford: Clarendon Press Publication; 1995.
  • Petryshyn WV. Approximation-solvability of nonlinear functional and differential equations. New York: Marcel Dekker; 1993.
  • Rothe EH. Introduction to various aspects of degree theory in Banach spaces. Vol. #23. Providence, RI: A.M.S.; 1986. (Math. Survey Monograph).
  • Browder FE. Degree of mappings for nonlinear mappings of monotone type: densely defined mapping. Phys Sci. 1983;80:2408–2409.
  • Browder FE. Fixed point theory and nonlinear problems. Bull Amer Math Soc. 1983;9:1–39. doi: 10.1090/S0273-0979-1983-15153-4
  • Berkovits J, Mustonen V. On the topological degree for perturbations of linear maximal monotone mappings and applications to a class of parabolic problems. Rend Mat Appl. 1992;12:597–621.
  • Kittilä A. On the topological degree for a class of mappings of monotone type and applications to strongly nonlinear elliptic problems. Ann Acad Sci Fenn Ser A I Math Diss. 1994;91:48.
  • Kartsatos AG, Skrypnik IV. Topological degree theories for densely defined mappings involving operators of type (S+). Adv Differ Equat. 1999;4:413–456.
  • Zhang SS, Chen YC. Degree theory for multivalued (S)-type mappings and fixed-point theorems. Appl Math Mech. 1990;11:409–421.
  • Adhikari DR, Kartsatos AG. Strongly quasibounded maximal monotone perturbations for the Berkovits Mustonen topological degree theory. J Math Anal Appl. 2008;348:122–136. doi: 10.1016/j.jmaa.2008.07.009
  • Adhikari DR, Kartsatos AG. A new topological degree theory for perturbations of the sum of two maximal monotone operators. Nonlinear Anal. 2011;74:4622–4641. doi: 10.1016/j.na.2011.04.023
  • Asfaw TM, Kartsatos AG. A Browder topological degree theory for multi-valued pseudomonotone perturbations of maximal monotone operators. Adv Math Sci Appl. 2012;22(1):91–148.
  • Asfaw T. A new topological degree theory for pseudomonotone perturbations of the sum of two maximal monotone operators and applications. J Math Anal Appl. 2016;434(1):967–1006. doi: 10.1016/j.jmaa.2015.09.035
  • Asfaw TM. New surjectivity results for perturbed weakly coercive operators of monotone type in reflexive Banach spaces. Nonlinear Anal. 2015;113:209–229. doi: 10.1016/j.na.2014.10.007
  • Asfaw TM, Kartsatos AG. New results for perturbations of locally defined generalized pseudomonotone operators in Banach spaces. Adv Math Sci Appl. 2014;24(1):1–10.
  • Kartsatos AG, Skrypnik IV. A new topological degree theory for densely defined quasibounded (S~+)-perturbations of multivalued maximal monotone operators in reflexive Banach spaces. Abstr Appl Anal. 2005;2005(2):121–158. doi: 10.1155/AAA.2005.121
  • Browder FE, Hess P. Nonlinear mappings of monotone type in Banach spaces. J Funct Anal. 1972;11:251–294. doi: 10.1016/0022-1236(72)90070-5
  • Kenmochi N. Nonlinear operators of monotone type in reflexive Banach spaces and nonlinear perturbations. Hiroshima Math J. 1974;4:229–263. doi: 10.32917/hmj/1206137159
  • Adhikari DR. Existence results for multivalued operators of monotone type in reflexive Banach spaces. Electron J Differ Equ Conf. 2017;24:1–10.
  • Adhikari DR. Nontrivial solutions of inclusions involving perturbed maximal monotone operators. Electron J Differ Equ. 2017;2017(151):21.
  • Adhikari DR, Kartsatos AG. Invariance of domain and eigenvalues for perturbations of densely defined linear maximal monotone operators. Appl Anal. 2016;95(1):24–43. doi: 10.1080/00036811.2014.996873
  • Ma T. Topological degree for set-valued compact vector fields in locally convex spaces. Dissertationes Math. 1972;92:1–43.
  • Adhikari DR, Kartsatos AG. Topological degree theories and nonlinear operator equations in Banach spaces. Nonlinear Anal. 2008;69(4):1235–1255. doi: 10.1016/j.na.2007.06.026
  • Kartsatos AG, Skrypnik IV. New results in the perturbation theory of maximal monotone and m-accretive operators in Banach spaces. Trans Amer Math Soc. 1996;348(5):1663–1707. doi: 10.1090/S0002-9947-96-01654-6
  • Hu S, Papageorgiou N. Generalizations of Browder's degree. Trans Amer Math Soc. 1995;347:233–259.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.