Existence of positive solutions for nonlinear third-order three-point boundary value problems

Positive solutions for a system of third-order differential equation with multi-point and integral conditions

“…The particularity of our method is in establishing the equation (1.1)-(1.2) so that the boundary conditions involve multipoint integral boundary conditions. Our work is new and more general than [7], [8]. For example, (1.7)-(1.8) is established for the following case n = 1,…”

“…, p}. Various types of boundary value problems were studied by many authors using fixed point theorems on cones, fixed point index theory, upper and lower solutions method, differential inequality, topological transversality and Leggett-Williams fixed point theorem [2], [3], [4], [5], [6], [7], [8], [11].…”

Several Existence Theorems of Monotone Positive Solutions for Third-Order Multipoint Boundary Value Problems

“…By using Guo-Krasnoselskii fixed point theorem, Guo et al [2] investigated the existence of at least one positive solution for the boundary value problems…”

“…By using the Leray-Schauder continuation theorem, the coincidence degree theory, Guo-Krasnoselskii fixed point theorem, the Leray-Schauder nonlinear alternative theorem, and upper and lower solutions method, many authors have studied certain boundary value problems for nonlinear third-order ordinary differential equations. We refer the reader to [1][2][3][4][5][6][7] and references cited therein. By using the LeraySchauder nonlinear alternative theorem, Zhang et al [1] studied the existence of at least 2 Boundary Value Problems one nontrivial solution for the following third-order eigenvalue problems:…”

Positive solutions for a nonlinear third order multipoint boundary value problem

“…Guo, Sun and Zhao [Guo et al 2008] studied the positive solutions of the third order three-point problem…”