Positive solutions for third-order Sturm Liouville boundary value problems with p-Laplacian

In this paper, by using the fixed point index method, we establish the existence of at least one or at least two positive solutions for the third-order Sturm Liouville boundary value problem with p-Laplacian 8>< >: . p.u00.t///0 C f .t; u.t// D 0; t 2 .0; 1/; u.0/ 􀀀 u0.0/ D 0; u.1/ C u0.1/ D 0; u00.0/ D 0 where p.s/ D jsjp􀀀2s; p > 1. As an application, an example is given to demonstrate the main result.