ISSN:
1572-9141
Keywords:
Differential operators
;
linear differential equation of third order
;
canonical forms
;
adjoint equation
;
cyclic permutation
;
oscillatory solution
;
Kneser solution
;
property A
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022878804065
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