R. Duduchava and T. Tsutsunava
abstract:
The purpose of the present research is to investigate the Fredholm criteria for
the Prandtl-type integro-differential equation with piecewise-continuous
coefficients in the Bessel potential spaces $\mathbb{H}^s_p(\mathbb{R})$.
We reduce the integro-differential equations to an equivalent system of Mellin
type convolution equation. Applying the recent results to Mellin convolution
equations with meromorphic kernels in Bessel potential spaces obtained by
V. Didenko & R. Duduchava [3] and R. Duduchava [9], the Fredholm criteria (and
in some cases, the unique solvability criteria) of the above-mentioned integro-differential
equations are obtained.
Mathematics Subject Classification: Primary 47B35; Secondary 45E10, 35J57
Key words and phrases: Integro-differential equations, Quasilocalization, Fredholm property, Symbol, Bessel potential spaces, Mellin convolutions