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Keywords:
principal solution; linear Hamiltonian system; reciprocal system
principal solution; linear Hamiltonian system; reciprocal system
Summary:
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.
References:
[1] Ahlbrandt C.D.: Principal and antiprincipal solutions of selfadjoint diferential systems and their reciprocals. Rocky Mountain J. Math. 2 (1972), 169-189. MR 0296388
[2] Ahlbrandt C.D.: Equivalent boundary value problems for self-adjoint differential systems. J. Diff Equations 9 (1971), 420-435. MR 0284636 | Zbl 0218.34020
[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 0618771
[4] Coppel W.A.: Disconjugacy. Lecture Notes in Math. No. 220 (1971), Berlin – New York – Heidelberg. MR 0460785 | Zbl 0224.34003
[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 1189218
[7] Hartman P.: Self-adjoint, non-oscillatory systems of ordinary, second order linear differential equations. Duke J. Math. 24 (1956), 25-35. MR 0082591
[8] Rasmussen C.H.: Oscillation and asymptotic behaviour of systems of ordinary linear differential equations. Trans. Amer. Math. Soc. 256 (1979), 1-49. MR 0546906
[9] Reid W.T.: Sturmian Theory for Ordinary Differential Equations. Springer Verlag, New York – Berlin – Heidelberg, 1980. MR 0606199 | Zbl 0459.34001
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