The Existence Of Positive Solutions For Two Classes Of Nonlinear Singular Third-Order Two-Point Boundary Value Problems On The Half-Line

This paper mainly studies the following two classes of nonlinear singular thirdorder two-point boundary value problems on the half-line and Assuming ?:(a,+?)?(0,+?)continuous,f:[a,+?)×(0,+?)?(0,+?)continuous in problem(?),and may be singular at time variable t=a.In problem(?)assuming that ?:[0,+?)?[0,+?)continuous,f:[0,+?)×(0,+?)×R2?R continuous,and may be singular at time variable t=0.In this paper,we will comprehensively apply the truncation function technique,the Arzela-Ascoli theorem,the diagonalization method together with nonlinear alternative to obtain the existence theorem of concave monotonically increasing positive solution for the first class of singular boundary value problem(?),and the existence of convex monotonically increasing positive solution for the second class of singular boundary value problem(?)are obtained.Finally,as an application of the obtained results,four examples will be given to show the validity of the obtained results.