Sharp conditions for the existence of positive solutions for a second-order singular impulsive differential equation

Existence of C1‐Positive Solutions for a Class of Second‐Order Impulsive Differential Equations

“…But in their work, a key assumption is that the nonlinearity f(t, x) is nondecreasing with respect to x ≥ 0. Clearly, if f(t, x) � t 2 x 1/3 + t 3 x − 1/3 , the results obtained in [9,10] are not valid. e aim of this study is to extend the results in [10] to more general cases.…”

“…Clearly, if f(t, x) � t 2 x 1/3 + t 3 x − 1/3 , the results obtained in [9,10] are not valid. e aim of this study is to extend the results in [10] to more general cases. We establish necessary and sufficient conditions for the existence of C 1 -positive solutions for a class of second-order impulsive differential equations.…”

“…In 2019, Ma and Zhang in [9] proved sharp conditions for the existence of positive solutions of secondorder singular differential equation with integral boundary conditions. Recently, Zhang and Tian [10] established sharp conditions for the existence of positive solutions of secondorder impulsive differential equations. But in their work, a key assumption is that the nonlinearity f(t, x) is nondecreasing with respect to x ≥ 0.…”

Positive solutions to second-order singular nonlocal problems: existence and sharp conditions

“…At the same time, we notice that a type of problem on sharp conditions has received much attention, for instance, see [62][63][64][65][66][67][68][69] and the references cited therein. Specially, by the compressing fixed point theorem, Yang [65] gave the sharp conditions for the existence of positive solutions for the following second-order differential equation:…”

Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems

“…Impulsive differential equation is regarded as a critical mathematical tool to provide a natural description of observed evolution processes (see [1][2][3][4]). So the consideration of impulsive differential equations has gained prominence and many authors have begun to take a great interest in the subject of impulsive differential equations, for example, see [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and the references cited therein.…”