Cauchy problem, boundary value problems with a boundary value condition and Sturm-Liouville problems related to the operator differential equation $X^{(2)}-AX=0$ are studied for the general case, even when the algebraic equation $X^2-A=0$ is unsolvable. Explicit expressions for the solutions in terms of data problem are given and computable expressions of the solutions for the finite-dimensional case are made available.
@article{104478,
author = {Lucas J\'odar and Enrique A. Navarro},
title = {Explicit solutions for boundary value problems related to the operator equations $X^{(2)}-AX=0$},
journal = {Applications of Mathematics},
volume = {36},
year = {1991},
pages = {409-416},
zbl = {0748.34013},
mrnumber = {1134918},
language = {en},
url = {http://dml.mathdoc.fr/item/104478}
}
Jódar, Lucas; Navarro, Enrique A. Explicit solutions for boundary value problems related to the operator equations $X^{(2)}-AX=0$. Applications of Mathematics, Tome 36 (1991) pp. 409-416. http://gdmltest.u-ga.fr/item/104478/
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