Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New results for the Nonoscillatory Asymptotic Behavior of High Order
  Differential Equations of Poincar\'e type   In this paper we study the asymptotic behavior of nonoscillatory solutions
for high order differential equations of Poincar\'e type. We introduce two new
and more weak than classical hypotheses on the coefficients, which implies a
well posedness result and a characterization of asymptotic behavior for the
solution of the Poincar\'e equation. The proof of the main results is based on
the application of the scalar method. We define a change of variable to reduce
the order of Poincar\'e type equation and deduce that the new variable
satisfies a nonlinear differential equation. We apply the variation of
parameters method and the Banach fixed point theorem to get the well posedness
and asymptotic behavior of the nonlinear equation. Then, by rewritten the
results in terms of the original variable we establish the existence of a
fundamental system of solutions for and we precise the formulas for the
asymptotic behavior of the Poincar\'e type equation.

22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics