Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 56, pp. 1-16.

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

Authors: Johnny Henderson (Baylor Univ., Waco, TX, USA)
         Abdelghani Ouahab (Sidi-Bel-Abbes Univ., Algeria)
	 Samia Youcefi  (Sidi-Bel-Abbes Univ., Algeria)

Abstract:
 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
 $$\displaylines{
 (\phi(y'))' = f(t,y(t)),  \quad\hbox{a.e. }  t\in [0,b],\cr
 y(t^+_{k})-y(t^-_k)=I_{k}(y(t_{k}^{-})), \quad k=1,\dots,m,\cr
 y'(t^+_{k})-y'(t^-_k)=\bar I_{k}(y'(t_{k}^{-})), \quad k=1,\dots,m,\cr
 y(0)=A,\quad  y'(0)=B,
 }$$
 where  $0=t_0<t_1<\dots<t_m<t_{m+1}=b$,  $m\in\mathbb{N}$.
 The functions $I_k, \bar I_k$ 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.

Submitted January 20, 2012. Published April 06, 2012.
Math Subject Classifications: 34A37, 34K45.
Key Words: phi-Laplacian; fixed point theorems; impulsive solution;
           compactness.