Existence Theory For Multiple Solutions Of Nonlinear Singular Three-point Boundary Value Problems For Second-order Impulsive Differential Equations

In this paper, existence theory for two positive solutions is presented to singular three-point boundary value problemThe function q(t) may be singular at t = 0 and the function / may be singular at y=0. I_k:[0,∞)→[0,∞) is continuous and nondecreasing,△y'|_t=tk=y'(t_k+0)-y'(t_k-0), where y'(t_k+0)( respectively y'(t_k-0)) denote the right limit (respectively left limit) of y'(t) at t = t_k.positive solutions is obtained via the Leray-Schauder alternative and the fixed point theorem in cones.