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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the dimension and the index of the solution set of nonlinear equations


Author: P. S. Milojević
Journal: Trans. Amer. Math. Soc. 347 (1995), 835-856
MSC: Primary 47H15; Secondary 35J65, 47N20, 58E07
MathSciNet review: 1282894
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Abstract: We study the covering dimension and the index of the solution set to multiparameter nonlinear and semilinear operator equations involving Fredholm maps of positive index. The classes of maps under consideration are (pseudo) $ A$-proper and either approximation-essential or equivariant approximation-essential. Applications are given to semilinear elliptic BVP's.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1282894-6
PII: S 0002-9947(1995)1282894-6
Keywords: Multiparameter continuation problems, covering dimension, index, approximation-essential maps, equivariant maps, (pseudo) $ A$-proper maps, elliptic BVP's
Article copyright: © Copyright 1995 American Mathematical Society