Abstract
The concept of zero-epi mapping is similar to the concept of topological degree but more refined and simpler.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Reference
BANAS, J. and GOEBEL, K. 1. Measure ofNoncompactness in Banach Spaces. Lecture Notes in Pure and Applied Mathematics, Nr. 60, Marcel Dekker Inc., New York, Basel, (1980).
BOURBAKI, N. 1. Topologi Générale. Chap. 9, Hermann, Paris, France (1971).
DARBO, G. 1. Punti uniti in transformazioni a codominio non compato. Rend. Sem. Math. Univ. Padova 25 (1955), 84–92.
DING, Z. 1. An infinite dimensional 0-epi mapping with degree zero. J. Math. Anal. Appl., 199 (1996), 458–468.
DUGUNDJI, J. and GRANAS, A. 1. Fixed Point Theory. Pwn-Polish Scientific Publishers, Warszawe (1982).
EDELSON, A. L. and PERA, M. P. 1. A note on nonlinear problems depending on infinite dimensional parameters. Nonlinear Anal. Theory Meth. Appl., 6 (1982), 1185–1191.
ERDELSKY, P. J. 1. Computing the Brouwer degree. Mathematics of Comput. 27 (1973), 133–137.
FURI, M., MARTELLI, M. and VIGNOLI, A. 1. Stable-solvable operators in Banach spaces. Atti. Accad. Naz. Lincei Rend. 1 (1976), 21–26.
FURI, M., MARTELLI, M. and VIGNOLI, A. 2. Contributions to the spectral theory for nonlinear operators in Banach spaces. Annali Mat. Pura Appl. 118 (1978), 229–294.
FURI, M., MARTELLI, M. and VIGNOLI, A. 3. On the solvability of nonlinear operators equations in normed spaces. Annali Mat. Pura Appl., 124 (1980), 321–343.
FURI, M. and PERA, M. P. 1. On the existence of an unbounded connected set of solutions for nonlinear equations in Banach. Atti Accad Naz. Lincei Rend. 67, 1–2 (1979), 31–38.
FURI, M. and PERA, M. P. 2. An elementary approach to boundary value problems at resonance. Nonlinear Anal. Theory, Meth. Appl. 4, Nr. 6 (1980), 1081–1089.
FURI, M. and PERA, M. P. 3. On unbounded branches of solutions for nonlinear operator equations in the nonbijurcation case. Boll. Un. Mat. Ital . 1-B (1982), 919–930.
FURI, M. and PERA, M. P. 4. Co-bifurcating branches of solutions for nonlinear eigenvalue problems in Banach spaces. Annali Mat. Pura Appl., 135 (1983), 119–132.
FURI, M AND VIGNOLI, A. 1. Unbounded nontrivial branches of eigenfunetions for nonlinear equations. Nonlinear Anal. Theory, Meth. Appl. 6 Nr. 11 (1982), 1267–1270.
FURI, M., PERA, M. P. and VIGNOLI, A. 1. Components of positive solutions for nonlinear equations with several parameters. Boll. Un. Mat. Ital. Serie Vi, Vol 1-C Nr. 1 (1982), 285–302.
GRANAS, A. 1. The theory of compact vectorfields and some applications to the theory offunctional spaces. Rozprawy Matematyczne, Warszawa, 30 (1962).
HYERS, D. H., ISAC, G. and RASSIAS TH. M. 1. Topics in Nonlinear Analysis and Applications. World Scientific, Singapore, New Jersey, London (1997).
ISAC, G. 1. (0, k)-Epi mappings. Applications to complementarity theory. In: Topics in Nonlinear Operator Theory (Eds. R. P. Agarwal and D. O’Regan (In printing)
IZE, J., MASSABO, I., PEJSACHOWICZ, J. and VIGNOLI, A. 1. Structure and dimension ofglobal branches of solutions to multiparameter nonlinear equations. Trans. Amer. Math. Soc. 201 Nr. 2 (1985), 383–486.
KRASNOSELSKII, M. A. 1. Positive solutions of Uperator Equations. P. Noordhoff, Groningen, The Netherlands, (1964).
LLOYD, G. 1. Degree Theory. Cambridge Tracts in Mathematics, Nr. 73 (1978).
MASSABO, I., NISTRI, P. and PERA, M. P. 1. A result on the existence of infinitely many solutions of a nonlinear elliptic boundary value problem at resonance. Boll. Un. Mat. Ital., (5) 17-A (1980), 523–530.
O’NEIL, T. and THOMAS, J. W. 1. The calculation of the topological degree by quadrature. Siam J. Num., Anal. 12 (1975), 673–680.
PANG, J. S. and YAO, J. C. 1. On a generalization of a normal map and equation. Siam, J. Control Opt., 33 Nr. 1 (1995), 168–184.
PERA, M. P. 1. Sulla risolubilite di equazioni non lineari in spazi di Banach ordinati. Boll. Un. Mat. Ital., 17-B (1980), 1063–1075.
PERA, M. P. 2. A topological method for solving nonlinear equations in Banach spaces and some related results on the structure of the solution sets. Rend. Sem. Mat. Univers. Politecn., Torino, 41 Nr. 3 (1983), 9–30.
PERA, M. P. 3. Unbounded components of solutions of nonlinear equations at resonance, with applications to elliptic boundary value problems. Boll. Un. Mat. Ital. 2-B (1983), 469–481.
PRÜFER, M. and SIEGBERG, H. W. 1. On computation aspects of degree in Rn. In: Functional Differential Equations and Approximation of Fixed Points (Eds. H. O. Peitgen and H. O Walter), Springer-Verlag, (1979).
STENGER, F. 1. Computing the topological degree ofa mapping in Rn. Numerische Mathamtik, 25 (1975), 23–28.
STYNES, M. J. 1. An Algorithm for the Numerical Calculation of the Degree of a Mapping. Oregon State University, Ph. D. Thesis (1977).
TARAFDAR, E U. and THOMPSON, H. B. 1. On the solvability of nonlinear, noncompact operator equations. J. Austral. Math. Soc. (Serie A) 43 (1987), 103–126.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Isac, G. (2000). Zero-Epi Mappings and Copmlementarity. In: Topological Methods in Complementarity Theory. Nonconvex Optimization and Its Applications, vol 41. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3141-5_7
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3141-5_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4828-1
Online ISBN: 978-1-4757-3141-5
eBook Packages: Springer Book Archive