Abstract
For implicit functions determined by the equation Tx+F(λ,x)=0, where T is an unbounded operator, existence and differentiability conditions are established. As an application, the solvability conditions for equations of the form Tx+f(x)=0 are derived.
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 248, 1998, pp. 216–224.
Translated by L. Yu. Kolotilina.
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Yakovlev, M.N. Implicit functions determined by equations with unbounded operators and the solvability of operator equations. J Math Sci 101, 3355–3360 (2000). https://doi.org/10.1007/BF02672778
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DOI: https://doi.org/10.1007/BF02672778