Serovaĭskiĭ, S. Ya. Differentiation of inverse functions in spaces without norm. (English. Russian original) Zbl 1107.58300 Funct. Anal. Appl. 27, No. 4, 290-292 (1993); translation from Funkts. Anal. Prilozh. 27, No. 4, 84-87 (1993). From the text: We establish the extended differentiability of the inverse operator in topological linear spaces for the case in which the conditions of the inverse function theorem may be violated. As an example we establish the generalized derivative of a solution \(x=x(y)\) of the Dirichlet problem for the equation \(-\Delta x+|x|^\rho x=y\) on an open bounded set \(\Omega\subset\mathbb R^n\), where \(x\in H^1_0\cap L_{\rho+2}\equiv X\), \(\rho>0\), \(y\in X'\). Cited in 3 Documents MSC: 58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds 46G05 Derivatives of functions in infinite-dimensional spaces Keywords:extended Gâteaux derivative × Cite Format Result Cite Review PDF Full Text: DOI References: [1] S. Ya. Serovaiskii, Izv. Vyssh. Uchebn. Zaved., Ser. Mat. No. 12, 55-63 (1991). [2] S. Ya. Serovaiskii, Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 4, 61-69 (1989). [3] N. Bourbaki, Topological Vector Spaces [Russian translation], Moscow, Inostr. Liter. (1959). [4] J.-L. Lions, Some Methods for Solving Boundary Value Problems [Russian translation], Moscow, Mir (1972). [5] J.-L. Lions, Usp. Mat. Nauk, No. 4, 15-46 (1973). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.