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

Abstract

This paper studies the existence of extremal solutions for a class of singular boundary value problems of second order impulsive differential equations. By using the method of upper and lower solutions and the monotone iterative technique, criteria of the existence of extremal solutions are established.

Multiple solutions of boundary-value problems for impulsive differential equations

“…There has been increasing interest in the investigation for boundary-value problems of nonlinear impulsive differential equations during the past few years and many literature have been published about the existence of solutions for first-order or second-order impulsive differential equations, see [1--10] and the references therein. There are some common techniques to approach these problems: the fixed point theorems [1,6,8,10]; the method of upper and lower solutions [3--5, 9]; the topological degree theory [7,11]; and so on [12]. It should be noted that compared to boundary-value problems for ordinary differential equations, there exist very less of multiplicity results for corresponding impulsive equations [1,10].…”

Existence of positive solutions for nonlocal second-order boundary value problem with variable parameter in Banach spaces

“…The existence of positive solutions for second-order boundary value problems has been studied by many authors using various methods (see [1][2][3][4][5][6]). Recently, the integral boundary value problems have been studied extensively.…”

Nagumo type existence results of Sturm–Liouville BVP for impulsive differential equations

“…For the general aspects of impulsive differential equations, we refer the reader to the classical monographs [7][8][9]. In recent years, boundary value problem (BVP) of nonlinear impulsive differential equations have received a considerable attention; see [10][11][12][13][14][15][16][17][18][19][20]9,21,22] and the references therein. The purpose of the present paper is to investigate the existence of solutions for the following Sturm-Liouville boundary value problem impulse effect…”