Faried, N., Rashed, L., Ahmed, A., Labeeb, M. (2019). Solvability of initial-boundary value problem of a multiple characteristic fifth-order operator-differential equation. test, 27(1), 1-7. doi: 10.1186/s42787-019-0036-7
Nashat Faried; Labib Rashed; Abdel Baset I. Ahmed; Mohamed A. Labeeb. "Solvability of initial-boundary value problem of a multiple characteristic fifth-order operator-differential equation". test, 27, 1, 2019, 1-7. doi: 10.1186/s42787-019-0036-7
Faried, N., Rashed, L., Ahmed, A., Labeeb, M. (2019). 'Solvability of initial-boundary value problem of a multiple characteristic fifth-order operator-differential equation', test, 27(1), pp. 1-7. doi: 10.1186/s42787-019-0036-7
Faried, N., Rashed, L., Ahmed, A., Labeeb, M. Solvability of initial-boundary value problem of a multiple characteristic fifth-order operator-differential equation. test, 2019; 27(1): 1-7. doi: 10.1186/s42787-019-0036-7

Solvability of initial-boundary value problem of a multiple characteristic fifth-order operator-differential equation

Journal of the Egyptian Mathematical Society
Volume 27, Issue 1, 2019, Pages 1-7    PDF (440.47 K)
DOI: 10.1186/s42787-019-0036-7
Authors
Nashat Faried; Labib Rashed; Abdel Baset I. Ahmed; Mohamed A. Labeeb
Helwan University, 11865 Cairo, Egypt
Abstract
In this study, we establish existence-uniqueness of a vector function in appropriate
Sobolev-type space for a boundary value problem of a fifth-order operator differential
equation. Proper conditions are obtained for the given problem to be well-posed.
Much effort is devoted to develop the association between these conditions and the
operator coefficients of the investigated equation. In this paper, accurate estimates of
the norms of the intermediate derivatives operators are presented and used to
determine the solvability conditions.
 
Keywords
Initial-boundary value problems; Operator-differential equation; Self-adjoint operator; Intermediate derivative operator
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