Abstract
Consider the third order differential operator L given by \(L\left(\cdot\right) \equiv \frac{1}{{a_3 (t)}}\frac{d}{{dt}}\frac{1}{{a_2 (t)}}\frac{d}{{dt}}\frac{1}{{a_1 (t)}}\frac{d}{{d(t)}}\left(\cdot\right)\) and the related linear differential equation L(x)(t) + x(t) = 0. We study the relations between L, its adjoint operator, the canonical representation of L, the operator obtained by a cyclic permutation of coefficients a i , i = 1,2,3, in L and the relations between the corresponding equations.
We give the commutative diagrams for such equations and show some applications (oscillation, property A).
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Cecchi, M., Došlá, Z. & Marini, M. Some properties of third order differential operators. Czechoslovak Mathematical Journal 47, 729–748 (1997). https://doi.org/10.1023/A:1022878804065
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DOI: https://doi.org/10.1023/A:1022878804065