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

Abstract EN

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 ft,z1,z2,z3,z4 to have superlinear or sublinear growth in zi, i=1,2,3,4.