NON-INTERLACED SOLUTIONS OF 2-DIMENSIONAL SYSTEMS OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS

作者：Le Gal O^*; Sanz F; Speissegger P

来源：Proceedings of the American Mathematical Society, 2013, 141(7): 2429-2438.

DOI：10.1090/S0002-9939-2013-11614-X

• Ordinary differential equations
• o-minimal structures

We consider a 2-dimensional system of linear ordinary differential equations whose coefficients are definable in an o-minimal structure R. We prove that either every pair of solutions at 0 of the system is interlaced or the expansion of R by all solutions at 0 of the system is o-minimal. We also show that if the coefficients of the system have a Taylor development of sufficiently large finite order, then the question of which of the two cases holds can be effectively determined in terms of the coefficients of this Taylor development.

• 出版日期2013-7