Singular Dirichlet problem for ordinary differential equation with impulses

Singular periodic impulse problems

“…To our knowledge, up to now singular periodic impulsive problems have not been treated. For singular Dirichlet impulsive problems we refer to the papers by Rachůnková [14], Rachůnková and Tomeček [17] and Lee and Liu [8].…”

Multiplicity of positive solutions to M-point boundary value problem of second order impulsive differential equations

“…Recently, impulsive differential equations have been studied extensively in the literatures (see [2,3,[6][7][8][9][10]12] and the reference therein). However, to the best of our knowledge, most of those papers studied the two-point or periodic Boundary value problems of impulsive differential equations.…”

“…There are two most common methods to deal with this kind of problems. The first one is the lower and upper solution method with the monotone iterative technique (see [2,7,10]), while the second one is to use Krasnoselskii s fixed point theorem in a suitable cone (see [3,6]). …”

Study of singular boundary value problems for second order impulsive differential equations

“…There have appeared numerous papers on impulsive differential equations during the last ten years. Many of them are on boundary value problems, see [5,6,8,[15][16][17][18][19][21][22][23][24][25][26][27][28]30], and it is interesting to note that some of them are about comparatively new applications like ecological competition, respiratory dynamics, vaccination strategies, see [3,7,9,13,29,[31][32][33].…”

“…the cases of singularities in the space variable by [1,21,30] and the cases of singularities in t = 0 and t = 1 by [15,16,22]. The main purpose of this paper, on the contrary to the mentioned papers, is not only to obtain existence results, but to prove the existence of extremal solutions.…”