Electron. J. Differential Equations, Vol. 2021 (2021), No. 93, pp. 1-16.

Monotone solutions of first order nonlinear differential systems

Lianwen Wang, Abdulrahman Mubarak

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
DOI: https://doi.org/10.58997/ejde.2021.93

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Lianwen Wang
School of Computer Science and Mathematics
University of Central Missouri
Warrensburg, MO 64093, USA
email: lwang@ucmo.edu
Abdulrahman Mubarak
Department of Mathematics
Kuwait University, P.O. Box 5969
Safat- 3060, Kuwait
email: abdulrahman.mubarak@ku.edu.kw

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