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On the existence of sulutions of the equation Lx ∞ Nx and a coincidence degree theory
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics / Volume 28 / Issue 2 / September 1979
- Published online by Cambridge University Press:
- 09 April 2009, pp. 139-173
- Print publication:
- September 1979
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- Article
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The coincidence degree for the pair (L, N) developed by Mawhin (1972) provides a method for proving the existence of solutions of the equation Lx = Nx where L: dom L ⊂ X → Z is a linear Fredholm mapping of index zero and
is a (possiblv nonlinear) mapping and Ω is a bounded open subset of X, X and Z being normed linear spaces over the reals. In this paper we have extended the coincidence degree for the pair (L, N) to solve the equation 
, where L: dom L ⊂ X → Z is a linear Fredholm mapping of index zero, 
and X, Z and Ω are as above, CK(Z) being the set of compact convex subsets of Z.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 47 H 15, 47 A 50; secondary 47 H 10, 47 A 55.
is a (possiblv nonlinear) mapping and Ω is a bounded open subset of 
and 