Geodesic
Explicit solutions for boundary value problems related to the operator equations $X^{(2)}-AX=0$
Applications of Mathematics, Tome 36 (1991) no. 6, pp. 409-416.

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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.
DOI : 10.21136/AM.1991.104478
Classification : 34A05, 34B05, 34B10, 34G10, 47A60, 47A62, 47N20
Keywords: Sturm-Liouville; operator differential equation; operator algebraic equation; Cauchy problems; boundary value problems 
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     title = {Explicit solutions for boundary value problems related to the operator equations $X^{(2)}-AX=0$},
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Jódar, Lucas; Navarro, Enrique. Explicit solutions for boundary value problems related to the operator equations $X^{(2)}-AX=0$. Applications of Mathematics, Tome 36 (1991) no. 6, pp. 409-416. doi : 10.21136/AM.1991.104478. http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104478/

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