Certain nonlocal boundary-value problems for linear differential operators

Boundary value problem for abstract first order differential equation with integral condition

“…The estimate (12) means that ũ(t) − u(t) → 0 as B → 0. Thus, the solutions of well-posed problem (1), (2) are stable under small perturbations of (1).…”

“…More general nonlocal conditions for different types of partial differential equations were considered later (see, e.g., [3][4][5][6][7][8][9]12,[14][15][16]). The present paper is devoted to the study of a boundary value problem for abstract first order linear differential equation with integral boundary conditions.…”

Elliptic problems with nonlocal boundary conditions and Feller semigroups

“…Bitsadze [7,8], Gushchin [42], Gushchin and Mikhailov [43,44], Eidelman and Zhiratau [14], Il'in and Moiseev [47], Kishkis [50,51], Paneah [67], Roitberg and Sheftel' [73,74], Soldatov [78], and others studied different versions and generalizations of nonlocal problems containing transformations of variables that mapped a boundary to closure of the domain. Special attention was devoted to the solvability nonlocal problems.…”

A nonlinear nonlocal mixed problem for a second order pseudoparabolic equation

“…An interesting collection of nonlocal parabolic problems in one-dimensional space is discussed in Fairweather [12]. Problems for elliptic equations with operator nonlocal conditions were considered by Scubachevski [25], Paneiah [22]. Then Gordeziani and Avalishvili [13], Mesloub and Bouziani [18], Mesloub and Lekrine [19], Pulkina [23], Beilin [1] devoted some papers to nonlocal problems for hyperbolic equations.…”