Positive solutions of nonlinear third-order boundary value problems involving Stieltjes integral conditions

Authors’ abstract: In this paper, by using the Guo-Krasnoselskii theorem, we investigate the existence and nonexistence of positive solutions of a class of boundary value problem of third-order nonlinear differential equation involving Stieltjes integral conditions. Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution respectively. An example is given to illustrate the main results of the paper.