Abstract:

The existence of positive solutions are obtained for boundary value problems of impulsive differential equation
            -y″(t)=f(t,y(t)), t∈［0,1］＼｛t₁,t₂,…,t_m｝,
             Δy′(tk)=J_k(y(t_k)), k=1,…,m,
             y(0)=y(1)=0
where f can change the sign. The proof is based on the fixed point index theorem in cones. The results of this paper improve and generalize the known results in the literature.

Key words: boundary value problem; fixed point index; impulsive differential equation