Positive solutions of periodic boundary value problems for nonlinear first-order impulsive differential equations Original Research Article

Motivated by Liu [Y. Liu, Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations, J. Math. Anal. Appl. 327 (2007) 435–452], Li et al. [X. Li, X. Lin, D. Jiang, X. Zhang, Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects, Nonlinear Anal. 62 (2005) 683–701] and Liu and Ge [Y. Liu, W. Ge, Stability theorems and existence results for periodic solutions of nonlinear impulsive delay differential equations with variable coefficients, Nonlinear Anal. 57 (2004) 363–399], this paper is concerned with the periodic boundary value problem (PBVP for short) for the nonlinear impulsive differential equation View the MathML source{x′(t)+a(t)x(t)=f(t,x(t)),a.e.t∈[0,T]∖{t1,…,tp},Δx(tk)=x(tk+)−x(tk)=Ik(x(tk)),k=1,…,p,x(T)=x(0). Turn MathJax on We obtain new sufficient conditions for the existence of at least one, two or three positive solutions of the above PBVP, respectively. Examples are presented to illustrate the main results.