Higher-order linear matrix descriptor differential equations of Apostol-Kolodner type.

Kalogeropoulos, Grigoris I.; Karageorgos, Athanasios D.; Pantelous, Athanasios A.

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In this paper we consider Bessel equations of the type $t^{2} X^{(2)} (t) + t X^{(1)} (t) + (t^{2} I - A^{2}) X (t) = 0$ , where A is an n $\times$ n complex matrix and X(t) is an n $\times$ m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.

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