A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.
Table of Contents
Equations of Barbashin type: differential equations in Banach spaces; Barbashin equations in the space C; Barbashin equations in Lebesgue spaces; Barbashin equations in ideal spaces. Theory of linear Barbashin equations: stability of solutions; continuous dependence on parameters; bounded and periodic solutions; degenerate kernels; stationary boundary value problems; non-stationary boundary value problems; general properties; operators in spaces with mixed norm; partial integral operators in the space C; spectral properties; linear partial integral equations. Generalizations and applications: generalized equations of Barbashin type; nonlinear equations and operators; the Newton-Kantorovich method; applications of Barbashin equations; applications of partial integral equations.