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Existence of solutions of Hammerstein equations of compact type

Published online by Cambridge University Press:  24 October 2008

Ronald I. Becker
Ronald I. Becker
Affiliation:
University of Cape Town
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Abstract

The existence of solutions is considered for equations of the form

for x ∈ H (a Hilbert space), P a compact linear operator on H; Q(x) a bounded linear operator on H and continuous in x and uniformly bounded; g(x) a continuous uniformly bounded map with range in H. Two situations are considered: Q(x) lies in a weakly compact set of operators for which (a) (I − PQ(x)) is invertible (non-resonance case) or (b) (I − P(Q(x) + λI)) is invertible for 0 < λ ≤ α (resonance case).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 149 - 158
Copyright
Copyright © Cambridge Philosophical Society 1981

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