Existence and topological structure of solution sets for phi-Laplacian impulsive differential equations

In this article, we present results on the existence and the topological structure of the solution set for initial-value problems for the first-order impulsive differential equation $$displaylines{ (phi(y'))' = f(t,y(t)), quadhbox{a.e. } tin [0,b],cr y(t^+_{k})-y(t^-_k)=I_{k}(y(t_{k}^{-})), quad k=1,dots,m,cr y'(t^+_{k})-y'(t^-_k)=ar I_{k}(y'(t_{k}^{-})), quad k=1,dots,m,cr y(0)=A,quad y'(0)=B, }$$ where $0=t_0