Geodesic
Continuous and generalized solutions of singular integro-differential equations in Banach spaces
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 11 (2012), pp. 62-74

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Continuous and generalized solutions of singular equations in Banach spaces are studied. We apply Lyapunov–Schmidt's ideas and the generalized Jordan sets techniques and reduce partial differential-operator equations with the Fredholm operator in the main expression to regular problems. In addition the left and right regularizators of singular operators in Banach spaces and fundamental operators in the theory of generalized solutions of singular equations are constructed.
Keywords: singular PDE, regularizators, fundamental operator-function.
Mots-clés : distributions 
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     author = {N. A. Sidorov and M. V. Falaleev},
     title = {Continuous and generalized solutions of singular integro-differential equations in {Banach} spaces},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {62--74},
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     number = {11},
     year = {2012},
     language = {en},
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N. A. Sidorov; M. V. Falaleev. Continuous and generalized solutions of singular integro-differential equations in Banach spaces. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 11 (2012), pp. 62-74. http://geodesic.mathdoc.fr/item/VYURU_2012_11_a6/