Abstract
The purpose of this paper is to develop a theory for differential equations with doubly-periodic coefficients analogous to the classic Floquet theory for differential equations with singly periodic coefficients. Unlike the classical theory the role of the exponent
v
of the differential equation is fundamental. If
v
takes integral values the analogous theory is well known and goes back to the work of Hermite in 1877. When
v
is rational the theory depends essentially on whether a certain number theoretic conjecture proposed by F. M. Arscott and G. P. Wright in 1969 is true. The paper resolves the conjecture and brings the doubly-periodic Floquet theory to some degree of completion.
Reference5 articles.
1. Arscott F. M. 1964 Periodic differential equations. Oxford: Pergamon Press.
2. Arscott F. M. & Sleeman B. D. 1968
3. Arscott F. M. & Wright G. P. 1969
4. Acta arith. 30, 229-240. J .Lond. math;Conway J. H.;Soc.,1976
5. S pisyprirFak. Univ. Brne 5 111-124.
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献