Positive Solutions for a Fourth-Order Riemann–Stieltjes Integral Boundary Value Problem

Yujun Cui, Donal O'Regan, Jiafa Xu
2019 Mathematical Problems in Engineering  
In this paper, we use the fixed point index to study the existence of positive solutions for the fourth-order Riemann–Stieltjes integral boundary value problem −x4t=ft,xt,x′t,x″t,x″′t, t∈0,1x0=x′0=x″′1=0,x″0=αx″t, where f: 0,1×ℝ+×ℝ+×ℝ+×ℝ+⟶ℝ+ is a continuous function and αx″ denotes a linear function. Two existence theorems are obtained with some appropriate inequality conditions on the nonlinearity f, which involve the spectral radius of related linear operators. These conditions allow
more » ... ions allow ft,z1,z2,z3,z4 to have superlinear or sublinear growth in zi, i=1,2,3,4.
doi:10.1155/2019/3748631 fatcat:6agkwsqibzhphn6zx3re2g3ehu