Nirenberg-type problems in Banach lattices

• Autorzy: Duma A. , Duma I.
• Języki publikacji: EN

Abstrakty

EN

A slightly modified version of the celebrated Nirenberg problem concerning expanding maps is considered. A positive answer is given for a type of lattice-expansive operators in discrete Hilbert lattices. Our approach is motivated by the study of the infinite systems of nonlinear equations.

Słowa kluczowe

EN

topological degree; surjection theorem; Banach lattice; expanding map; Nirenberg problem

PL

stopnie topologiczne; twierdzenie surjektywne; przestrzeń Banacha; problem Nirenberga

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2010
• Tom: Vol. 16, nr 2
• Strony: 189--197
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Duma A.

autor

Duma I.

• Department of Mathematics, University of Craiova, A. I. Cuza str. 13, Craiova 200585 Dolj, Romania,

Bibliografia

• [1] K.-C. Chang, Methods in Nonlinear Analysis, Springer Monographs in Mathematics, 2005.
• [2] K.-C. Chang, L. Shujie, A remark on expanding maps. Proceedings of the AMS, Vol. 85 (1982), No. 4, pp. 583-586.
• [3] J. E. Hernandez, M. Z. Nashed, Global invertibility of expanding maps. Proceedings of the AMS, Vol. 116 (1992), No. 1, pp. 285-291.
• [4] L. V. Kantorovich, G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.
• [5] A. G. Kartsatos, On the connection between the existence of zeros and the asymptotic behavior of resolvents of maximal monotone operators in reflexive Banach spaces. Transactions of the AMS, Vol. 350 (1998), No. 10, pp. 3967-3987.
• [6] P. Meyer-Nieberg, Banach lattices. Springer-Verlag, New York, 1991.
• [7] J.-M. Morel, H. Steinlein, On a problem of Nirenberg concerning expanding maps. Journal of Functional Analysis, Vol. 59 (1984), No. 1, pp. 145-150.
• [8] J. Szczepanski, On a problem of Nirenberg concerning expanding maps in Hilbert space. Proceedings of the AMS, Vol. 116 (1992), No. 4. pp. 1041-1044.
• [9] J. Szczepanski, A new result on the Nirenberg problem for expanding maps. Nonlinear Analysis TMA, Vol. 43(2001), No. 1, pp. 91-99.