Geodesic
Almost solubility of classes of non-linear integral equations of the first kind on cones
Izvestiya. Mathematics , Tome 83 (2019) no. 5, pp. 990-1007

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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, equation of the first kind, solubility.
Mots-clés : tangent cone 
@article{IM2_2019_83_5_a3,
     author = {M. Yu. Kokurin},
     title = {Almost solubility of classes of non-linear integral equations of the first kind on cones},
     journal = {Izvestiya. Mathematics },
     pages = {990--1007},
     publisher = {mathdoc},
     volume = {83},
     number = {5},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_5_a3/}
}
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M. Yu. Kokurin. Almost solubility of classes of non-linear integral equations of the first kind on cones. Izvestiya. Mathematics , Tome 83 (2019) no. 5, pp. 990-1007. http://geodesic.mathdoc.fr/item/IM2_2019_83_5_a3/