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Solution branches for mappings in cones, and applications

Published online by Cambridge University Press:  17 April 2009

E.N. Dancer
Affiliation:
Department of Mathematics, University of New England, Armidale, New South Wales.
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Abstract

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We prove the existence of global solution branches for positive mappings. This improves an earlier result of the author. We also prove a related result for mappings in wedges. We then use these two results to prove the existence of solutions for boundary-value problems for systems of ordinary differential equations.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Amann, Herbert, “Fixed points of asymptotically linear maps in ordered Banach spaces”, J. Functional Analysis 14 (1973), 162171.Google Scholar
[2]Борнсович, Ю.Г. [Borisovič, Ju.G.], “О точках бифуркации положительных и полуположительных операторов” [The bifurcation points of positive and semipositive operators], Kazan. Gos. Univ. Učen. Zap. 127 (1967), kn. 1, 3541.Google ScholarPubMed
[3]Dancer, E.N., “Global solution branches for positive mappings”, Arch. Rational Mech. Anal. 52 (1973), 181192.Google Scholar
[4]Dancer, E.N., “Global structure of the solutions of non-linear real analytic eigenvalue problems”, Proc. London Math. Soc. (3) 27 (1973), 747765.CrossRefGoogle Scholar
[5]Dancer, E.N., “On the structure of solutions of non-linear eigenvalue problems”, Indiana Math. J. (to appear).Google Scholar
[6]Goldberg, Seymour, Unbounded linear operators (McGraw-Hill, New York, 1966).Google Scholar
[7]Krasnosel'skii, M.A., Topological methods in the theory of nonlinear integral equations (translated by Armstrong, A.H.. International Series of Monographs on Pure and Applied Mathematics, 45. Pergamon, Oxford, London, New York, Paris, 1964).Google Scholar
[8]Nussbaum, Roger D., “The fixed point index for local condensing maps”, Ann. Mat. Pura Appl. 89 (1971), 217258.CrossRefGoogle Scholar
[9]Rabinowitz, Paul H., “Some global results for nonlinear eigenvalue problems”, J. Functional Analysis 7 (1971), 487513.Google Scholar
[10]Turner, R.E.L., “Transversality and cone maps”, preprint.Google Scholar