Abstract
The existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using a fixed point theorem in cone, we obtain two existence results, which extend some known results.
Highlights
1 Introduction In this paper, we discuss the existence of positive periodic solutions for the following second order impulsive differential equation: u (t) + (a – b)u (t) + f (t, u(t)) =, t = tk, ( . )
To define the solution of ( . ), we introduce the space PCr(R) = {u : R → R|u(j)(t) is continuous at t = tk, left continuous at t = tk, and each u(j)(tk+) exists for k ∈ Z, where j =, . . . , r}
It should be noted that compared to first order impulsive differential equations, there exist very few existence results of positive periodic solutions for second order impulsive equations, especially for second order impulsive equations with derivative term, see [ – ]
Summary
1 Introduction In this paper, we discuss the existence of positive periodic solutions for the following second order impulsive differential equation: u (t) + (a – b)u (t) + f (t, u(t)) = , t = tk, One cannot obtain the multiplicity of periodic solutions under their conditions.
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