Almost solubility of classes of non-linear integral equations of the first kind on cones

Using convexity properties of the images of completely continuousnon-linear integral operators, we describe the closed convex cones lyingeither in the recessive cone, or in the tangent cone of the closed imageof the operator being studied (depending on the nature of the integrand).These cones are determined by the principal part of theasymptotics of the integrand at infinity, independently of the variation ofthe subordinate part. We discuss applications to the generalized solubilityof non-linear integral equations of the first kind.

non-linear integral operator, recessive cone, tangent cone, equation of the first kind, solubility