On the Qualitative Behaviors of Solutions of the Sunflower-Type Equation with Multiple Constant Delays

This paper investigates several qualitative behaviors of the solutions for a class of second-order nonlinear delay differential equations (DDEs) characterized by multiple constant delays. Applying the Lyapunov–Krasovskii (LK) approach, together with LaSalle’s Invariance Principle, we derive new conditions for stability when p(t,x,y)≡0 and boundedness and integrability whenever p(t,x,y) is non-zero. The results obtained generalize some existing theorems in the literature to the case of multiple delay configurations, accommodating a wider class of sunflower-type equations.