## M. V. Falaleev and N. A. Sidorov

# Continuous and Generalized Solutions of Singular Partial Differential Equations

## (*Lobachevskii Journal of Mathematics, Vol.20, pp.31-45*)

The paper discusses continuous and
generalized solutions of equations with partial derivatives having
the operator coefficients which operate in Banach spaces. The
operator with the elder derivative with respect to time is
Fredholm. We apply Lyapunov--Schmidt's ideas and the generalized
Jordan sets techniques to reduce partial differential-operator
equations with the Fredholm operator in the main part to regular
problems.
In addition this technique has been exploited to prove the theorem
of existence and uniqueness for a singular initial-value problem, as
well as to construct the left and right regularizators of singular
operators in Banach spaces and to construct fundamental operators in
the theory of generalized solutions of singular equations.

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