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Solvability of nonlinear equations in a cone of a banach space

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Abstract

The solvability conditions for the equation Tu+F(u)=0 are found in the case where the operator [T+F′(u)]−1 exists only for u∈K, where K is a cone in a Banach space X. An application concerning the solvability of boundary-value problems for systems of second-order differential equations is provided.

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  1. M. N. Yakovlev
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 248, 1998, pp. 225–230.

Translated by L. Yu. Kolotilina.

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Yakovlev, M.N. Solvability of nonlinear equations in a cone of a banach space. J Math Sci 101, 3361–3364 (2000). https://doi.org/10.1007/BF02672779

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  • DOI: https://doi.org/10.1007/BF02672779

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