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On the solvability of nonlinear noncompact operator equations

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  09 April 2009

E. U. Tarafdar ,
H. B. Thompson  and
R. O. Vyborny
E. U. Tarafdar
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Queensland, Australia 4067
H. B. Thompson
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Queensland, Australia 4067
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Abstract

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The notion of (p, k)-epi mappings is introduced. The properties of such mappings are studied and the results obtained are applied to some differential equations.

Keywords

admissible mappingp-epi(p, k)-epik-set contractionmeasure of unsolvability

MSC classification

Secondary: 47H10: Fixed-point theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 1 , August 1987 , pp. 103 - 126
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Furi, M., Martelli, M. and Vignoli, A., ‘On the solvability of nonlinear operator equations in normed spaces’, Ann. Mat. Pura Appl. 124 (1980), 321–343.CrossRefGoogle Scholar
[2]Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order (Springer-Verlag, New York, 1983).Google Scholar
[3]Gokhberg, I. C., Goldstein, L. S. and Markus, A. S., ‘Investigation of some properties of bounded linear operators in connection with q-norms’, Uchen. Zap. Kishinev. Gos. Univ. 29 (1957), 29–36.Google Scholar
[4]Granas, A., ‘The theory of compact vector fields and some applications to the theory of functional spaces’, Rozprawy Matematyezne, Warszawa, 30 (1962).Google Scholar
[5]Hartman, P. and Wintner, A., ‘On hyperbolic partial differential equations,’ Amer. J. Math. 74 (1952), 834–864.CrossRefGoogle Scholar
[6]Kuratowski, K., ‘Sur les espaces comptets’, Fund. Math. 15 (1930), pp. 301–319.CrossRefGoogle Scholar
[7]Lloyd, N. G., Degree theory (Cambridge University Press, London, 1978).Google Scholar
[8]Martin, Robert H. Jr., Nonlinear operators and differential equations in Banach spaces (John Wiley and Sons, New York, 1976).Google Scholar
[9]Nussbaum, R. D., ‘The fixed point index for local condensing maps’, Ann. Mat. Pura Appl. 124 (1971), 217–258.CrossRefGoogle Scholar
[10]Vainberg, M. M., Variational methods for the study of nonlinear operators (Holden-Day Inc., London, 1964).Google Scholar