R. Duduchava and T. Tsutsunava

Integro-Differential Equations of Prandtl Type in the Bessel Potential Spaces

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