Solvability of Degenerating Hyperbolic Differential Equations with Unbounded Operator Coefficients

Abstract

We consider initial value problems for a number of hyperbolic equations with a power-law degeneracy and with operator coefficients in a Banach space and establish sufficient conditions for the unique solvability of these problems in terms of the coefficients of the equation, the degeneracy order, and the initial elements.

Uniqueness Criterion for Solutions of Nonlocal Problems on a Finite Interval for Abstract Singular Equations

“…In the next section, we will consider nonlocal problems for the class of so-called degenerate equations. Note that the Cauchy problem for such a class of degenerate equations was investigated above in [26].…”