Positive solutions of the three-point boundary value problem for second order differential equations with an advanced argument

Solutions and Green’s functions for some linear second-order three-point boundary value problems

“…The expression of the Green's function in Theorem 3.1 is simpler, see [3,4,[13][14][15], so that the unique solution of the linear problem is denoted easily, the format of the equivalent nonlinear integral equation is dapper and its property can be discussed conveniently. …”

“…The solutions of some boundary value problems for linear ordinary differential equations can be denoted by its Green's function, see [1][2][3][4]. Some boundary value problems for nonlinear differential equations can be transformed into the nonlinear integral equations the kernel of which are the Green's functions of corresponding linear differential equations.…”

Positive solutions for nonlinear operator equations and several classes of applications

“…Because of the crucial role played by nonlinear equations in applied science as well as in mathematics. Moreover, nonlinear functional analysis has been an active area of research, and nonlinear operators which arise in the connection with nonlinear differential and integral equations have been extensively studied over the past several decades (see [1,2,4,6,14,30,33]). The existence and uniqueness of positive solutions for nonlinear operator equations is very important in theory and applications.…”

Positive solutions for semi-positone three-point boundary value problems

“…Since then, more general nonlinear three-point boundary value problems have been studied by many authors with much of the attention given to positive solutions. For a small sample of such work, we refer the reader to works [7,11,12,17]. The results of these papers are based on the Leray-Schauder continuation theorem, the nonlinear alternative of Leray-Schauder, the coincidence degree theory of Mawhin, Krasnoselskii's fixed point theorem, Schauder fixed point theorem, fixed point theorems in cones and so on.…”