Difference equations: disconjugacy, principal solutions, Green’s functions, complete monotonicity

Hartman, Philip

doi:10.1090/S0002-9947-1978-0515528-6

Difference equations: disconjugacy, principal solutions, Green’s functions, complete monotonicity
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Trans. Amer. Math. Soc. 246 (1978), 1-30 Request permission

Abstract:

We find analogues of known results on nth order linear differential equations for nth order linear difference equations. These include the concept of disconjugacy, Pólya’s criterion for disconjugacy, Frobenius factorizations, generalized Sturm theorems, existence and properties of principal solutions, signs of Green’s functions, and completely monotone families of solutions of equations depending on a parameter.

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Aufgaben und Lehrsätzen aus der Analysis

Thomas L. Sherman, Properties of solutions of $n\textrm {th}$ order linear differential equations, Pacific J. Math. 15 (1965), 1045–1060. MR 185185, DOI 10.2140/pjm.1965.15.1045

Theory of Bessel functions