Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 93, pp. 1-16.

Title: Monotone solutions of first order nonlinear differential systems
       
Authors: Lianwen Wang (Univ. of Central Missouri, Warrensburg, MO, USA)
         Abdulrahman Mubarak (Kuwait Univ.,  Safat, Kuwait)

Abstract:
This article concerns the classification, continuablity, boundedness, and existence
of solutions for a system of first order nonlinear differential equations.
First, we prove that all solutions of the system are eventually monotonic and can
be separated into two classes. Then we discuss the continuability of solutions.
After that we establish necessary and sufficient conditions for the boundedness of
all solutions. Also, we study the existence of monotone solutions in certain classes.

Submitted August 7, 2020. Published November 23, 2021.
Math Subject Classifications: 34C11, 34C12.
Key Words: Monotone solutions; system of differential equations; boundedness;
           nonlinear; existence; continuability