Principal solutions and transformations of linear Hamiltonian systems
Archivum mathematicum, Tome 28 (1992) no. 1-2, pp. 113-120 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Sufficient conditions are given which guarantee that the linear transformation converting a given linear Hamiltonian system into another system of the same form transforms principal (antiprincipal) solutions into principal (antiprincipal) solutions.
Sufficient conditions are given which guarantee that the linear transformation converting a given linear Hamiltonian system into another system of the same form transforms principal (antiprincipal) solutions into principal (antiprincipal) solutions.
Classification : 34A25, 34C10, 34C20
Keywords: principal solution; linear Hamiltonian system; reciprocal system
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Došlý, Ondřej. Principal solutions and transformations of linear Hamiltonian systems. Archivum mathematicum, Tome 28 (1992) no. 1-2, pp. 113-120. http://geodesic.mathdoc.fr/item/ARM_1992_28_1-2_a13/

[1] Ahlbrandt C.D.: Principal and antiprincipal solutions of selfadjoint diferential systems and their reciprocals. Rocky Mountain J. Math. 2 (1972), 169-189. | MR

[2] Ahlbrandt C.D.: Equivalent boundary value problems for self-adjoint differential systems. J. Diff Equations 9 (1971), 420-435. | MR | Zbl

[3] Ahlbrandt C.D., Hinton D.B., Lewis R.T.: The effect of variable change on oscillation and disconjugacy criteria with application to spectral theory and asymptotic theory. J. Math. Anal. Appl. 81 (1981), 234-277. | MR

[4] Coppel W.A.: Disconjugacy. Lecture Notes in Math. No. 220 (1971), Berlin – New York – Heidelberg. | MR | Zbl

[5] Došlý O.: On transformation of self-adjoint linear differential systems and their reciprocals. Annal. Pol. Math. 50 (1990), 223-234.

[6] Došlý O.: Transformations of linear Hamiltonian system preserving oscillatory behaviour. Arch. Math. 27 (1991), 211-219. | MR

[7] Hartman P.: Self-adjoint, non-oscillatory systems of ordinary, second order linear differential equations. Duke J. Math. 24 (1956), 25-35. | MR

[8] Rasmussen C.H.: Oscillation and asymptotic behaviour of systems of ordinary linear differential equations. Trans. Amer. Math. Soc. 256 (1979), 1-49. | MR

[9] Reid W.T.: Sturmian Theory for Ordinary Differential Equations. Springer Verlag, New York – Berlin – Heidelberg, 1980. | MR | Zbl