Nonlinear Third-Order BVP With Advanced Arguments And Stieltjes Integral Boundary Conditions

In the field of chemical engineering, underground water flow, heat conduction, thermo-elasticity and plasma physics, lots of problems can be reduced to boundary value problems with integral boundary conditions. Recently, third-order boundary value problems (BVPs for short) with integral boundary conditions, which cover third-order multi-point BVPs as special cases, have attracted much attention from many authors.In this paper, we study the following BVP with advanced arguments and Stielt-jes integral boundary conditions λi(i=1,2) denotes a linear functional on C[0,1] given by involving a Stieltjes integral with a suitable function Ai(i= 1,2) of bounded varia-tion. It is important to indicate that it is not assumed that λi[u](i= 1,2) is positive to all positive u.In chapter 2, by using the Guo-Krasnoselskii fixed point theorem, we get the existence of at least one positive solution to this BVP; in chapter 3, we obtain the existence of multiple positive solutions to this BVP. The main tool used is the Avery-Peterson fixed point theorem.