| Summary: | 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 $0=t_0<t_1<dots<t_m<t_{m+1}=b$, $minmathbb{N}$. The functions $I_k, ar I_k$ characterize the jump in the solutions at impulse points $t_k$, $k=1,dots,m$. For the final result of the paper, the hypotheses are modified so that the nonlinearity $f$ depends on $y'$, but the impulsive conditions and initial conditions remain the same.
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