Solution of boundary value problems for a fourth-order equation with multiple characteristics in a semi-bounded domain by constructing the Green’s function
DOI:
https://doi.org/10.56143/ujmcs.v2i3s.9Keywords:
Fourth-order differential equations, multiple characteristics, semi-infinite domain, energy integral, Green’s function, functional series, uniform convergence, partial derivatives.Abstract
The subject of this study is boundary value problems in a semi-bounded domain for a fourth-order inhomogeneous differential equation with multiple characteristics. The uniqueness of regular solutions for the formulated problems is established using the energy integral method, while the existence theorems are justified by applying the classical method of separation of variables. The desired solutions are analytically expressed in the form of infinite functional series using the constructed Green’s function. Furthermore, the absolute and uniform convergence of both the solution series themselves and the series composed of the corresponding partial derivatives is rigorously proved within the considered geometric domains.
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