On Unique Solvability of a Multipoint Boundary Value Problem for Systems of Integro-Differential Equations with Involution

Abstract

In this paper, a multipoint boundary value problem for systems of integro-differential equations with involution has been studied. To solve the studied problem, the parameterization method is used. Based on the parametrization method, the studied problem is decomposed into two parts, i.e., into the Cauchy problem and a system of linear equations. Necessary and sufficient conditions for the unique solvability of the studied problem are determined.

Nonlinear Two-Point Boundary Value Problem for a Second Order Impulsive System of Integro-Differential Equations With Mixed Maxima

“…A lot of publications of studying on differential and integro differential equations with impulsive effects, describing many natural and technical processes, are appearing (see, for examples, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Two-point and multi-point boundary value problems for the differential and integro-differential equations are studied by many authors (see, for example [21][22][23][24]. Second-order differential equations with nonlocal boundary value conditions and impulsive effects are almost not studied.…”

Inverse problem for a second order impulsive system of integro-differential equations with two redefinition vectors and mixed maxima

“…Two-point and multi-point boundary value problems for the differential and integro-differential equations are studied by many authors (see, for example [26][27][28][29]). However, second-order differential equations with nonlocal boundary value conditions and impulsive effects are almost not studied.…”