New existence results for nonlinear delayed differential systems at resonance

Area of Science:

• Mathematics
• Differential Equations
• Nonlinear Analysis

Background:

• First-order delayed differential equations are crucial in modeling various phenomena.
• The existence of positive periodic solutions is a significant challenge in this field.
• Existing literature provides foundational methods but requires further development.

Purpose of the Study:

• To establish new existence theorems for positive periodic solutions.
• To investigate first-order delayed differential systems with specific periodic coefficients and delays.
• To extend the understanding of periodic solutions in dynamical systems.

Main Methods:

• Application of the fixed point theorem in cones.
• Analysis of first-order delayed differential systems with continuous ω-periodic functions.
• Rigorous mathematical formulation and proof techniques.

Main Results:

• Several novel existence theorems for positive periodic solutions are established.
• The conditions for the existence of such solutions are precisely defined.
• The findings expand the theoretical framework for delayed differential systems.

Conclusions:

• The study successfully demonstrates the existence of positive periodic solutions.
• The established theorems offer valuable contributions to the field of nonlinear analysis.
• This research enriches and complements existing knowledge on periodic solutions.