On the Unique Solvability of a Nonlocal Boundary-Value Problem for Systems of Loaded Hyperbolic Equations with Impulsive Actions

A Family of Two-Point Boundary Value Problems for Loaded Differential Equations

“…We note that condition 3) of Theorem 2 can also be formulated without using the fundamental matrix X(t) of the system of differential equations μ = A(t)μ. To do that, it is necessary to solve the problem (36), (37) by the parameterization method [25] splitting the segment [0, T ] with respect to the variable t. Earlier in the papers [15]- [18], one had established the conditions of unique resolvability of nonlocal problems for the system of loaded by the time variable t hyperbolic equations. Further, the results of Sections 2 and 3 will be applied to the study of questions of existence and uniqueness of the classical solution to the nonlocal problem for loaded by the spatial variable x hyperbolic equations with mixed derivatives.…”

On the Initial-Boundary Value Problem for System of the Partial Differential Equations of Fourth Order

“…We will investigate the questions of existence and uniqueness of the classical solutions to the initial-boundary value problem for system of the partial differential equations of fourth order (1)--(5) and the approaches of constructing its approximate solutions. For this goals, we applied the method of introduction additional functional parameters proposed in [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] for solving of various nonlocal problems for systems of hyperbolic equations with mixed derivatives. Considered problem is provided to nonlocal problem for the system of hyperbolic equations of second order including additional functions and integral relation.…”

Cauchy problem for a high‐order loaded integro‐differential equation

“…Initial and boundary value problems for loaded second‐ and third‐order equations of hyperbolic, parabolic, elliptic, and mixed types were investigated in the works of previous research 20–34 . We would like to note that problems for the loaded equations of high‐order differential equations have not been studied yet.…”

“…Initial and boundary value problems for loaded second-and third-order equations of hyperbolic, parabolic, elliptic, and mixed types were investigated in the works of previous research. [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] We would like to note that problems for the loaded equations of high-order differential equations have not been studied yet. The construction of a theory of unique solvability in the study of the correctness of problem formulation for the generalized multidimensional differential equation with loaded term is required both for the internal completeness of the theory of loaded differential equation and for numerous applications.…”