Abstract:
Using convexity properties of the images of completely continuous
non-linear integral operators, we describe the closed convex cones lying
either in the recessive cone, or in the tangent cone of the closed image
of the operator being studied (depending on the nature of the integrand).
These cones are determined by the principal part of the
asymptotics of the integrand at infinity, independently of the variation of
the subordinate part. We discuss applications to the generalized solubility
of non-linear integral equations of the first kind.
Keywords:non-linear integral operator, recessive cone, tangent cone, equation of the first kind, solubility.
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