Abstract
We prove local theorems on the existence of solutions of the Cauchy problem for singular equations of the form {fx262-01} in Banach spaces. Solvability conditions depend on the type of the singularity of the pencil λA + B of closed linear operators A and B. Examples and applications to finite-dimensional differential-algebraic equations, infinite systems of differential equations, and partial differential equations of the non-Kovalevskaya type are presented.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 225–239, February, 2008.
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Rutkas, A.G. Solvability of semilinear differential equations with singularity. Ukr Math J 60, 262–276 (2008). https://doi.org/10.1007/s11253-008-0057-0
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DOI: https://doi.org/10.1007/s11253-008-0057-0