The index and the asymptotic stability of fixed points in two dimensions: A counterexample

Nonlinear Analysis, Theory, Methods and Applications

Volumn 32, Issue 6, 1998, Pages 719-725

  Alonso, José Miguel ^a   Campos, Juan ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Asymptotic stability; Fixed points in two dimensions; Index

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; SET THEORY; THEOREM PROVING;

FIXED POINT INDEX; LIPSCHITZIAN HOMEOMORPHISM; PERIODIC DIFFERENTIAL EQUATIONS; POINCARE OPERATOR;

TOPOLOGY;

EID: 0032091478     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00520-8     Document Type: Article

References (5)

1. Ortega, R., Some applications of the topological degree to stability theory. In Topological Methods in Differential Equations and Inclusions, ed. A. Granas and M. Frigon. Kluwer Academic Publishers, Dordrecht, 1995, pp. 377-410.
2. Dancer, E. N., Upper and lower stability and index theory for positive mappings and applications. Nonlinear Analysis, 1991, 17, 205-217.
3. Ortega, R., A criterion for asymptotic stability based on topological degree. In Proceedings of the First World Congress of Nonlinear Analysts, Tampa, 1992, pp. 383-394.
4. Krasnoselskii, M. and Zabreiko, P. P., Geometrical Methods of Nonlinear Analysis. Springer-Verlag, Berlin, 1984.
5. Meyer, K. R. and Hall, G. R., Introduction to Hamiltonian Dynamical Systems and the N-Body Problem. Springer-Verlag, New York, 1992.